It extended Everton's unbeaten run to 10 in all competitions and they head into Tuesday's Merseyside derby at Anfield just two points behind Kenny Dalglish's side.
Spurs, conversely, have north London rivals Arsenal breathing down their necks and could see the gap to the fourth-placed Gunners cut to just a point on Monday night.
This was their third successive league defeat. The last manager to suffer that was Juande Ramos in October 2008 and it resulted in him being replaced by Harry Redknapp.
Tim Howard - 6.5
The American commanded his box well and never really looked tested despite Tottenham's attempts on goal, especially with their late onslaught. Confident when coming out to deal with crosses and shots.
Phil Neville - 7
A solid, hardworking performance from the Everton skipper to quell the threat of Modric down the flank. An excellent example of how a captain should stay calm and keep everything simple for his teammates to follow.
Leighton Baines 7.5
Baines displayed steady defending at the back and excellent vision when foraging ahead, setting up the through ball that eventually led to the opening goal. He has definitely done no harm to his chances of being picked as England's starting left back in the Euros.
Sylvian Distin - 7
Distin matched Adebayor like for like in the match, keeping the large, wiley Togolese striker quiet. Also, he was quick to respond when Baines was threatened to be overlapped by Gareth Bale or Walker, closing down the crosses before they become a threat.
John Heitinga - 7
Heitinga was there for almost all the crosses that managed to go into the Everton penalty box, positioning himself well to deny the sneaky and speedy Defoe before he can pounce on those passes. Had a few rash challenges, but was otherwise excellent.
Seamus Coleman (Off 82') - 5.5
Coleman was the only blip in what is an otherwise fine all-round performance from Everton. The 23-year-old's decision making was poor and he's lucky to have hardworking teammates to make up for his errors.
Marouane Fellaini - 7.5
Fellaini held his own in the midfield, easily pushing away Sandro's physical challenges and making clever interceptions. He kept everything simple and simplicity worked more effectively for Everton to keep their attack going.
Tim Cahill - 6
Deployed in a deeper role, Cahill was much quieter in this match but nevertheless helped as an outlet for his side to ease the pressure with his clever movement.
Leon Osman - 7
Osman was always chasing down the flank and providing an option for his teammates to counter attack. He created the opening goal for Jelavic after latching onto Baines' pass and cutting it back for Jelavic to fire home.
Royston Drenthe (Off 65') - 7.5
The on-loan midfielder from Real Madrid always looked dangerous when he had the ball on the flanks, always willing to take on defenders and threatening Friedel's goal.
Nikica Jelavic - 7
Everton finally found the striker they are looking for in Jelavic. For too long the Toffees have been deploying midfielders up front and the lack of finishing instinct has proven costly at times. Jelavic stepped up and sealed his home debut with a well taken first-time shot which left Friedel with absolutely no chance.
Jack Rodwell (On 65') - 6R
Rodwell provided an extra defensive layer to see the game out for Everton.
Denis Stracqualursi (78') - N/A
Phil Jagielka (82') - N/A
Brad Friedel - 6.5
Never really tested and not at fault for the goal conceded - it's a miracle itself that he managed to fly across goal to get a palm on the shot!
Kyle Walker - 5.5
Walker strangely resisted the instinct that saw him always bomb up in attack. He managed to keep Coleman from attacking down his flank but there was little he could do about Baines, who chose to send in his crosses early.
Younes Kaboul - 5
Guilty of ball-watching as Osman jinked pass him to set up Jelavic's goal but did well otherwise to hold his own in his own box otherwise.
Ledley King - 5.5
King could do little to prevent the goal and was otherwise unbothered throughout the match.
Benoit Assou-Ekotto - 5.5
He seems to miss linking up with Bale down the left flank and provided Modric little to work with on the overlap in the match. Defensively, he had a hard time, coming up against Drenthe but acquitting himself well to prevent the Dutchman from having an impact in the game.
Luka Modric - 5.5
A muted outing for Modric out in the flanks yet again has proven that the Croatian does not belong down the flanks. Modric looked brighter whenever he cut into the middle to link up with his teammates, though, and Redknapp should have played him inside instead.
Scott Parker - 6.5
Parker didn't have much say influence in terms of the usual defensive duties he carries out, leaving the tackling to Sandro instead. He tried to play the more forward role and was surprisingly good. Not as good as Modric, but still, he busted the myth that his passing range is equals to his spitting distance.
Sandro (Off 69') - 5
The Brazilian is clearly not the quality midfielder Tottenham need if they want to challenge for top honours. He relied on brute strength most of the time to barge into opposing midfielders and showed little promise in building up the attack.
Gareth Bale - 5
Bale was as effective down the right flank as he is right-legged. Which is to say, not at all. Everton had to simply push him out wide and Bale was forced to either turn back or cross with his weaker right foot.
Emannuel Adebayor (Off 55') - 5
Adebayor never really gotten into the groove of the game, hardly having a touch of the ball at all.
Jermain Defoe - 5
Defoe never stopped trying up front but lacked the killer touch in the box to help his side grab a goal back.
Louis Saha (On 55') - 6
Saha came close to scoring against his former side in injury time when he struck the crossbar and looked a lot more dangerous than Adebayor in the box.
Rafael van der Vaart (On 69') - 5.5
He came on to add more control to the midfield but by then Everton were willing to flood five men into the middle and van der Vaart couldn't do much to provide.
Jake Livermore - N/A