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 put them 2-1 up four minutes after the break but Boyce's own goal in the closing stages denied them three points.
Tottenham went in front in bizarre circumstances. 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.
Wigan 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.
The home side snatched the lead through McManaman's first Premier League goal. The 22-year-old forward cracked in an unstoppable effort from outside the area having collected the ball from James McCarthy.
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.
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 Tom Huddlestone.