Mido is close to agreeing a permanent deal with the club and rightly so after heading his side in front after 58 minutes.
And it was England midfielder Jenas who sealed the victory with his first goal since joining the club from Newcastle five minutes later with another well taken header.
If Tottenham keep performing like this they have every chance of pushing for a European place come the end of the season.
In contrast Everton's season is going from bad to worse after they suffered their sixth consecutive defeat which equals their worst ever start to a Premiership campaign.
David Moyes' side are rooted to the foot of the Premiership table and they will need James Beattie to find his goalscoring boots quickly if they are to avoid a season-long relegation battle.
Tottenham boss Martin Jol was able to welcome back Lee-Young Pyo, Michael Dawson and Michael Carrick from injury.
All three players missed the 3-2 win at Charlton, but Jol wasted no time calling them straight back into first-team action. He was also boosted by Mido shaking off the hamstring problem he suffered at The Valley.
Beattie had finally recovered from a long-term injury and was able to take his place on the Everton bench.
And it was the away side who almost broke the deadlock in the 15th minute. Marcus Bent made a neat turn inside the box before firing the ball just wide of the post.
Everton continued to mount pressure on the Spurs goal and just 60 seconds later, Paul Robinson had to be at his best to keep the scores level.
James McFadden turned two defenders on the edge of the area before unleashing a fierce drive which produced a fine save from the England goalkeeper diving away to his right.
Despite Everton's early dominance, it was Tottenham who came even closer to opening the scoring on 19 minutes.
The ever impressive Aaron Lennon crossed for Dawson whose close-range header was superbly kept out by Nigel Martyn in the Everton goal.
McFadden continued to cause problems for the Spurs defence and saw his 29th-minute cross fall kindly for Bent, but he could only send his header wide of the target.
The hosts had strong claims for a penalty turned down on 32 minutes when Lee looked to be brought down inside the box by Matteo Ferrari. But referee Dermot Gallagher ignored the appeals of the home supporters and waved for play to continue, awarding a goal-kick to the visitors.
Dawson must have thought it wasn't going to be his day on 35 minutes when he saw his close-range header cleared off the line. Carrick produced a pin-point corner which fell perfectly for the former Forest defender. But Dawson's powerful header was hacked clear by Nuno Valente.
Carrick's midfield partner Jenas then saw a 30-yard shot comfortably saved by Martyn.
Jermain Defoe had another golden chance 11 minutes after the break, but saw his fierce shot well saved by Martyn diving low down to his right.
Tottenham finally opened the scoring on 58 minutes. Joseph Yobo gave the ball away and Jenas' cross fell perfectly for Mido, who flashed his header into the top right hand corner.
Jenas added a second for the home side when Defoe's cross picked out the England midfielder and he made no mistake heading the ball past Martyn.
Paul Robinson had to be at his very best on 69 minutes when he made a fantastic finger-tip save to deny Everton substitute Duncan Ferguson.