By FOX Sports staff
Despite enjoying the lion's share of possession for much of the 90 minutes, the Bundesliga giants were unable to convert their chances as Willy Caballero produced an inspired display to keep the visitors at bay, twice making brilliant stops to deny Mario Gotze in the first half.
Instead, Dortmund will now head into next Tuesday's return leg at the Signal Iduna Park knowing that a goal for their Spanish opponents would drastically alter the complexion of the tie.
Here, FOX Sports takes a look at how Wednesday's match at La Rosaleda panned out.
Had it not been for Caballero, Malaga could easily have been on the receiving end of a comprehensive defeat as the veteran made a series of brilliant stops, including twice denying Gotze in one-on-one situations.
One of the reasons why Caballero had been so busy was the fact that both his centre-backs, Weligton and Martin Demichelis, struggled to keep up with the opposition attackers' constant off-the-ball movement, although the latter did do well in several occasions to weigh in with timely interceptions.
Jesus Gamez was however very impressive at right-back as he defended resolutely against both Kevin Grosskreutz and Marcel Schmelzer, yet still found the time to push forward in support.
Caballero - 8.5 | Gamez - 7.5 | Demichelis - 7 | Weligton - 6 | Antunes - 6.5
Along with Caballero, Jeremy Toulalan was a major reason why Malaga were able to salvage something out of Wednesday's game. The 29-year-old seemed to be on a one-man mission to keep Dortmund at bay, and shielded his backline with real authority.
He worked well in tandem with Manuel Iturra, although the Chilean was unable to provide his usual creative influence given the hosts were regularly pegged back in their own half.
While he's now 31, Joaquin certainly rolled back the years down the right as he gave Schmelzer all kinds of problems throughout the 90 minutes with his pace and skill, and resembled the sprightly young winger that burst onto the scene with Spain at the 2002 FIFA World Cup.
However, the one man that was expected to shine - Isco - failed to do so as he struggled to get involved despite showing one or two moments of quality. Many of Europe's leading clubs have been linked with a move for the talented 20-year-old, but they would do well to take note that this is not the first time he has failed to deliver on the big stage.
Joaquin - 8 | Toulalan - 8.5 | Iturra - 7 | Isco (off 87') - 6
Although Julio Baptista and Javier Saviola are now approaching the twilight of their careers, the ex-Real Madrid duo are still capable of punishing opponents when given half a chance.
The Brazilian started the brighter of the two and held up the ball well, but he gradually faded out of the game.
Saviola, on the other hand, regularly made his way in behind Felipe Santana and got into a number of excellent scoring opportunities, but he was just unable to find the telling finish.
Baptista (off 76') - 6.5 | Saviola (off 68') - 7
Brought on for Saviola with over 20 minutes to go, Francisco Portillo hardly touched the ball and it remains to be seen why Malaga coach Manuel Pellegrini didn't opt to bring on Roque Santa Cruz earlier.
Santa Cruz did eventually come on in the 76th minute, but he - like Duda who followed - did not have sufficient time to make any sort of impact.
Portillo (on 68') - 5.5 | Santa Cruz (on 76') - N/A | Duda (on 87') - N/A
Given Dortmund's dominance, it's easy to think that Roman Weidenfeller was hardly troubled but he did have to make a couple of smart saves as Malaga threatened with their brief forays forward.
Schmelzer, playing with a mask, was his usual energetic self on the left but Dortmund failed to get the same out of Lukasz Piszczek, who looked too worried about Isco to go about his usual game, and hardly ventured past his halfway line.
Neven Subotic did well to hold the fort for the Germans and he stepped in to make a number of intelligent interceptions, but Felipe Santana looked vulnerable at times, and is clearly not a like-for-like replacement for Mats Hummels in terms of quality.
Weidenfeller - 7.5 | Piszczek - 6 | Subotic - 7 | Santana - 6.5 | Schmelzer - 7.5
One thing that worked extremely well for BVB coach Jurgen Klopp was his deployment of Sebastian Kehl and Ilkay Gundogan in the engine room.
With their combination of defensive awareness, tenacity and distribution, the duo combined to form a wall right on the halfway line and initiated one attack after another as they picked up loose balls in the middle of the park.
Just ahead of time, Gotze absolutely tormented the Malaga defenders with his pace and skill on the ball, and had an excellent game even if he was the most wasteful player in front of goal.
Kehl (off 80') - 7 | Gundogan - 7 | Gotze (off 90') - 8
It was very strange to see Marco Reus hauled off nine minutes after the hour mark given he had been one of Dortmund's most dangerous players, and came close to scoring in the first half with a lovely freekick that sailed just wide.
Grosskreutz tried to offer his side the same penetration down the left but failed to get the better of Gamez, yet he was left on for the entire 90 minutes.
And although he is currently regarded as one of Europe's best strikers, Robert Lewandowski had an evening to forget as he struggled to perform even the simplest of tasks, like keeping the ball under control.
The Poland star did have a couple of good touches throughout the game, but the lofty standards he has set for himself in the past two seasons meant that his display on Wednesday was ultimately disappointing.
Reus (off 69') - 7.5 | Grosskreutz - 6 | Lewandowski - 5
After coming on for Reus, Julian Schieber showed good energy in the attacking third but he was hesitant at the crucial moment and wasted two good openings.
Sven Bender and Oliver Kirch both came on in the final ten minutes but had minimal time to influence proceedings.
Schieber (on 69') - 6.5 | Bender (on 80') - N/A | Kirch (on 90') - N/A