Robbie Keane's first-half penalty gave Spurs a deserved win and keeps Martin Jol's side on course for a place in next season's Champions League.
Robbie Keane kept Spurs on course for fourth place
Keane scored after he was hauled back by Everton defender Alan Stubbs.
Spurs' victory margin should have been greater against a poor Everton side, with keeper Richard Wright denying Jermaine Jenas and Jermain Defoe.
Defoe also struck the bar in the second half in front of watching England boss Sven-Goran Eriksson.
Spurs gave a rare start to Defoe alongside Keane, with Mido ruled out because of a groin injury.
And they dominated the first 45 minutes against an Everton side that appeared to be running down the clock on a mixed campaign.
The only surprise was that it took Spurs 33 minutes to break the deadlock, with Keane scoring from the spot after he had been dragged back by Stubbs.
Spurs made a switch at half-time, with former Liverpool midfield man Danny Murphy coming on for Teemu Tainio.
Everton's much-maligned keeper Wright kept his side in contention with a brilliant double save three minutes after the break.
He dived to his right to deny Jenas, then made a miraculous point-blank stop from Defoe after Gary Naysmith had inexplicably turned the ball into his path from only six yards out.
Spurs were guilty of wasting opportunities to score the crucial second goal and Keane fired wastefully over the top, with only Wright to beat after he was played in by Murphy.
Everton were still making little impression on the Spurs defence and boss David Moyes introduced Duncan Ferguson for Simon Davies after 66 minutes.
Defoe almost gave Spurs the second goal they deserved with 18 minutes left but his curling finish bounced back off the bar with Wright beaten.
Everton manager David Moyes:
"No complaints. Tottenham were the better side, probably as good as any side we have had at Goodison Park this year.
"Our lads tried everything they could but it didn't happen for us. Tottenham came here and showed why they are doing so well.
"We will keep going. We are paid well here and this is a great club to play for, so anybody who thinks the season is over will be found out. We won't have it here. We want to try and finish in the top 10."
Spurs head coach Martin Jol:
"This was a very important game and we are delighted to have won at a difficult place.
"Our aim is to make everybody happy at the club and the Premiership table has made good reading for a while.
"Everton are a strong side who play English football, but we coped with that. We pressed them and created chances.
"I am only disappointed we didn't score more goals from the chances we created. Everton didn't create a lot and we looked good."
Everton: Wright, Neville, Yobo, Stubbs (Ferrari 59), Naysmith (Kilbane 84), Osman, Carsley, Cahill, Davies (Ferguson 66), McFadden, Beattie.
Subs Not Used: Turner, Weir.
Booked: Carsley, Neville.
Tottenham: Robinson, Stalteri, Gardner, King (Davids 90), Lee, Lennon (Davenport 82), Carrick, Jenas, Tainio (Murphy 45), Keane, Defoe.
Subs Not Used: Cerny, Barnard.
Goals: Keane 33 pen.
Ref: H Webb (S Yorkshire).