By FOX Sports Staff
The Pole helped his side score the opener after converting a cross from Mario Gotze as early as within the seventh minute. Thereafter, he demonstrated terrific reflexes to convert two fortuituous chances in the second half to put his side firmly in command.
Only Cristiano Ronaldo seemed capable of answering for Madrid and the Portuguese grabbed one back shortly before halftime in what could turn out to be a vital away goal for the Spanish outfit.
However, the night belonged to Lewandowski who, not satisfied with being the first player to score a hat-trick against Madrid in the Champions League, converted a late penalty in order to make the prospect of an all-German final, the first of its kind, seem all but certain.
Madrid, though, can still take heart in Deportivo la Coruna's tremendous turnaround from a similar scoreline in the 2003/04 Champions League quarter-finals when they beat AC Milan 4-0 at the Riazor in the second leg.
FOX Sports analyses what went wrong for Jose Mourinho's men from a terrific night at the Signal Iduna Park and the results from the week's European fixtures clearly demonstrate the importance of traditional wingers as well as high fitness levels.
Neven Subotić was the star for the Dortmund defence as he kept the opponents at bay and made several tidy challenges and clearances.
The Serbian was a calm presence at the back and ensured that Mats Hummels' slip-up, the defender's weak backpass allowing Gonzalo Higuain to rifle in the cross that led to Ronaldo's goal, did not prove too costly in the end.
The duo of Marcel Schmelzer and Lucasz Piszczek were also quite handy up in attack as they regularly charged forward to provide much-needed support to Lewandowski.
In contrast, Weidenfeller had an easy game and was rarely called to action but he did have to carry out a crucial close-range block late into the game to deny Ronaldo a second goal.
Weidenfeller - 8 | Piszczek (off 83') - 8 | Subotic - 8.5 | Hummels - 7.5 | Schmelzer (off 83') - 8
Just like in defence, one man shone the brightest for the home side in midfield and that was Ilkay Gundogan. The 22-year-old was dominant in all departments - tackling, passing, marking, dribbling - and could have even scored a goal had a dipping shot not been saved by Diego Lopez in the second half.
Sven Bender was an able partner in midfield and it seemed that Jurgen Klopp had instructed both of them to keep a close watch on the likes of Ronaldo and Luka Modric and it ensured that Higuain was starved of any supply.
The other active midfielder for the home side was Jakub Blaszczykowski and the Pole seemed to have been instructed to play in something of a withdrawn role in order to assist Piszczek's task in marking Ronaldo.
Bender - 7.5 | Gundogan (off 91') - 8.5 | Blaszczykowski (off 82') - 8
If Lewandowski's agent is to be believed, the striker is set to leave the club in the summer transfer window but he appeared to be completely at ease in the Dortmund set-up on Wednesday night and did not look like a player angling for a move. He communicated well with his team-mates and was always in the right places in one of his best performances in a black-yellow shirt.
The tall striker used his length to good effect to convert Gotze's cross for the opener and his strength allowed him to shrug off the attentions of Raphael Varane to score two further goals later in the game. It was a pity, though, that he earned a yellow card for a foul as it was otherwise a flawless outing for the striker.
While both Gotze and Lewandowski will definitely be applauded for their contributions, Marco Reus should also get part of the praise as he exerted considerable influence on the Dortmund attack. The former Borussia Monchengladbach midfielder darted between the Madrid defenders with consummate ease and rained Lopez's goal with shots and through-balls, earning a penalty as well in the process.
His dribbling and intelligence completely disoriented the visitors' defence and also allowed Lewandowski to regularly sneak into dangerous positions in the second half.
Gotze - 8 | Reus - 8.5 | Lewandowski - 9.5
Dortmund's substitutions were brought on at a rather late stage into the game and they helped wind down the clock and preserve the three-goal lead.
Kehl (on 82') - N/A | Grosskreutz (on 83') - N/A | Schieber (on 91') - N/A
Letting in four goals would beg the question as to whether it was right to start with Lopez ahead of captain Iker Casillas. However, it'd be hard to pin the blame entirely on the ex-Sevilla goalkeeper as instead his defence were more culpable for the goals and it's always difficult to defend close-range strikes.
The Madrid defence were not coordinated enough on the night as noone seemed willing to take up the responsibility of man-marking Lewandowski. Varane was the only one who attempted to close down the Dortmund man with any regular frequency but the youngster lacked the strength to match up to the Poland international.
Pepe, in particular, had a poor game as he was repeatedly out of position and did not demonstrate adequate leadership in defence. Such guidance was needed as Sergio Ramos, the captain for the night, often ventured forward to join the attack but the Spain international lacked the necessary first touch and composure to control the ball for any length of time.
Left-back Fabio Coentrao was slightly better in that endeavour but, frustratingly, opted to feed the ball down the line to Ronaldo in a predictable fashion.
Lopez - 6 | Varane - 5 | Pepe - 4 | Ramos - 5 | Coentrao - 5.5
Both the defeats suffered by Madrid and Barcelona were the result of an absence of traditional wingers who could contribute both in defence and attack. Marauding full-backs can be dangerous against sides with weak defences but they prove to be a hindrance against powerful, pacey attacks that are fast on the break and intelligent in their distribution.
This was a lesson that Mourinho's midfield had to learn the hard way and the likes of Xabi Alonso and Luka Modric made it worse by being too narrow in their passing. They made it far too easy for Dortmund's defensive midfielders and Alonso, previously a master at long passes, sent many passes astray whenever he was put under pressure.
Mesut Ozil, in particular, was virtually anonymous for much of the game and needs to learn a thing or two from his compatriots about the importance of pressing and tackling.
Khedira - 7 | Ozil - 4 | Alonso (off 80') - 5.5 | Modric (off 68') - 5
Both Spanish sides also need to reduce their reliance on their star men as Ronaldo drifted to the same positions down the left flanks and made life easier for the Dortmund defence.
Nevertheless, Ronaldo was not daunted by the roughhouse tactics employed by Dortmund although he did waste a lot of time in unsuccessful free-kick appeals.
It can also be said that Ronaldo was lucky to score his goal as a defensive error on Hummel's part allowed him the opportunity to tap the ball in from close range. Worryingly, it means that Mourinho cannot expect his compatriot to deliver a hat-trick next week and therefore it is paramount that the rest of his charges step up to the plate in the return leg.
Gonzalo Higuain was also disappointing on the night and the Argentinean needs to be more than just a poacher and improve on his dribbling and passing. He did, however, do well to assist Ronaldo and the away goal could offer his side a meagre chance of reaching the final.
Ronaldo - 7 | Higuain (off 67') - 6
Despite having a star-studded bench, the likes of Kaka and Karim Benzema were not capable of matching up to the pace and industry demonstrated by the Borussians.
Angel di Maria will need to start in the second leg as the Argentinean, at the very least, is capable of sending in comparatively accurate crosses although he will need a target to aim at.
Benzema could also be given a stint as the Frenchman did backtrack and help out the midfield more often than Higuain did during his brief cameo.
Benzema (on 67') - 6 | Di Maria (on 68') - 6 | Kaka (on 80') - N/A