The Latics, 18th in the Barclays Premier League, would have moved out of the drop zone had they been able to hang on for victory.
But having come from behind to take the lead after conceding early on through a defensive mix-up, in the end their efforts were not quite enough for all three points.
Gareth Bale put Tottenham in front in the ninth minute, capitalising on some ponderous play by Maynor Figueroa and Joel Robles, but Wigan were level in the 11th thanks to Boyce's header.
Callum McManaman's excellent piledriver then put them 2-1 up four minutes after the break, but Boyce was unlucky to find the net again with an own-goal in the closing stages.
The result leaves Wigan two points adrift of 17th-placed Aston Villa, with both sides having four games left to play - including a meeting between them at the DW Stadium on the final day of the season.
Tottenham, meanwhile, stay fifth with four matches to go, level on points with fourth-placed Chelsea - who they have a game in hand over - and a point behind third-placed Arsenal.
Wigan's reshuffled defence, missing the injured Antolin Alcaraz, was facing a Tottenham attack in which Jermain Defoe had been restored to play alongside Bale, and Spurs' threat going forward was apparent from the off.
Tom Huddlestone delivered an early free-kick on to the head of Bale, who flicked the ball wide, and sent another one swerving against the post shortly after.
With the momentum behind them, it came as little surprise that it was Tottenham who subsequently opened the scoring, although the goal came about in bizarre circumstances and Wigan only really had themselves to blame.
A horribly hesitant exchange of passes between Figueroa and Robles led to the latter cannoning an attempted clearance against the outstretched leg of the approaching Bale, and the ball rebounded straight into the net.
It was a truly embarrassing moment for Roberto Martinez's men, but to their credit, they responded swiftly and within two minutes had equalised.
Shaun Maloney swung a corner in from the right and Boyce was on hand to crash a header past Hugo Lloris.
Tottenham looked to regain the initiative, with Scott Parker sending the ball over after playing a one-two with Bale, but Wigan looked galvanised and went close when Arouna Kone's ambitious, delicate side-foot shot from Jordi Gomez's tee-up went just too high.
Figueroa redeemed himself by making a great tackle to take the ball away from Defoe as the striker advanced towards goal, but the Honduran international appeared to injure his groin in doing so.
He was soon carried off on a stretcher, no doubt wondering about his chances of featuring in next month's FA Cup final against Manchester City, with Ronnie Stam taking his place, before Tottenham suffered an apparent injury blow of their own as Mousa Dembele had to be replaced by Lewis Holtby.
Spurs finished the first half strongly and after Bale had passed up a good-looking chance by heading over, Robles did well to palm the ball away from the feet of Defoe as the England man burst through the Wigan defence, which subsequently managed to clear up.
Having survived that scramble, the Latics emerged from the break looking bright and Lloris had to claw away a tricky ball from Stam.
Moments later Wigan fans were on their feet as the home side snatched the lead through what was McManaman's first Premier League goal - and a fine one at that.
The 22-year-old forward, who endured such widespread criticism after his controversial tackle on Newcastle's Massadio Haidara last month, cracked in an unstoppable effort from outside the area having collected the ball from James McCarthy.
Gomez - already on a yellow card - then appeared fortunate to escape further punishment when his studs connected with the head of Holtby.
Good defensive work from James McArthur allowed Robles to claim the ball with Clint Dempsey lurking, and Kone then twice failed to covert when he might have done better, hooking one shot straight into Lloris' arms after chesting the ball down and then seeing the Frenchman getting down to save another.
Di Santo, who had come on for McManaman, then sent an attempt off-target, and Wigan were made to rue their inability to add a further goal.
Tottenham - with the fit-again Aaron Lennon introduced from the bench - applied late pressure and it paid off in the 90th minute, with a low ball into the box bobbling in off the unfortunate Boyce.
And it might have been worse for Wigan had Robles not pulled off a save to keep out Bale's stoppage-time free-kick, the Spaniard then stopping a follow-up effort from Huddlestone before a shot from Defoe was blocked by a defender all in a few frantic final seconds.