Emmanuel Adebayor scored the game's only goal, stabbing home Kyle Walker's quickly taken free-kick on 65 minutes.
It condemned the Toffees to just a fourth Premier League defeat of the season, dropping them to sixth place in the Premier League.
Here's a look at some Everton-related talking points to emerge from this contest.
Everton silenced the home crowd with an impressive start, passing through Spurs with some clever touches and sharp, angled passes.
Tim Sherwood's side seemed disorganised and allowed the Toffees eight shots in the opening 38 minutes, three of which were on target.
Hugo Lloris produced a couple of smart saves to keep the game goalless, but Everton should have tested him more, missing the target from some inviting positions.
Ultimately, this lack of quality in the final third proved the difference. The Toffees failed to make their supremacy count and never had the same access to goal after half-time.
Leon Osman was most guilty during this opening burst, unable to score from four first-half shots.
Having spent most of the first half spurning chances, Everton then lost concentration and allowed Spurs to score with their first shot on target.
A free-kick was awarded on the halfway line, and as Kyle Walker ran up, neither Osman nor Gareth Barry prevented the right-back from taking it quickly.
Having hit it forward to Adebayor—poorly played onside by Sylvain Distin—Seamus Coleman was then outmuscled by the Togolese striker while Tim Howard was badly beaten at his near post.
In short, it was a very preventable goal to concede. The fact this was the home side's first attempt on target after 65 minutes of football will only exacerbate the Toffees' frustration further.
While Martinez clearly won the early tactical battle, formulating a plan that saw his side dominate the early stages, his substitutions weren't as successful—something he's often made a difference with at Everton.
In this match, however, a mixture of bad timing and strange choices proved costly.
First of all, Everton were enjoying increased space in front of Spurs' defence as the second half began. With Ross Barkley the ideal exponent of this, the youngster was drafted in on 64 minutes to exploit it further.
Moments later, Tottenham scored, enabling them to sit back and close off the space—essentially spoiling the point of Barkley's arrival.
Martinez then waited too long to bring on his final substitutions and the arrival of Gerard Deulofeu and Aiden McGeady gave Everton a threat out wide but little presence in the middle. Both needed a striker to link up with and work around.
Kevin Mirallas' late switch to a forward role didn't work (as we will come to), and the decision to include Lacina Traore on the substitute's bench—but not bring him on—was also peculiar.
With a heavily bolstered bench, Everton would have hoped for far more impact from their substitutions. As it was, the Toffees mustered just one solitary off-target attempt in the 25 minutes that followed Spurs' goal.
Kevin Mirallas can be an effective striker, but only in certain situations.
He is not suited to a lone role against a congested defence, as was the case against Aston Villa and in the latter stages of this match.
Chasing the game, he moved into this role for the final 15 minutes. Spurs put extra bodies behind the ball and Mirallas struggled to make any impression, often returning to a flank.
He needs space to work in and, ironically, the time he would have been best suited to this role would have been at the start of the second half, with Everton finding extra space in the final third.
If Traore was not going to come on, Everton should have perhaps stuck with Naismith in the middle to at least provide a presence to work around.
The closing stages saw Barkley, Deulofeu, McGeady and even Mirallas fighting for an opening out wide with nobody left in the box.
To pluck a positive for this deflating defeat, Everton's back four contained their opponents well, limiting Sherwood's side to very few chances.
Preventing a shot on target until 65 minutes away at a top-four rival is an impressive feat and both Jagielka and Distin were especially commanding throughout.
Everton's back five played every minute of the first 11 Premier League games this season, conceding just 10 goals. Since then, each individual has missed action through suspension or injury.
This was only the second time in 15 matches Martinez could select his favoured personnel at the back, something he will hope to do for the rest of the season.
Defeat saw the Toffees drop to sixth, five points behind their city rivals and two behind Spurs.
Liverpool are now red-hot favourites for fourth place, and it's hard to see the Toffees clawing back enough points to overtake both them and Spurs.
In the short term, Everton can at least take comfort from the fact they respond well to defeat under Martinez. Thus far, all four games to follow a loss have been won under their new manager/
Statistics via WhoScored.com