A howler from Wigan keeper Joel gifted Gareth Bale the opening goal after nine minutes, but Boyce headed the strugglers level just two minutes later.
Callum McManaman's superb goal early in the second half appeared likely to lift the Latics out of the bottom three until Tom Huddlestone's late free-kick came off Boyce to secure a point for Spurs in their bid to qualify for the UEFA Champions League.
Tottenham almost took the lead inside the opening five minutes when Huddlestone's free-kick from an acute angle caught Wigan by surprise, but came back off the post.
The visitors did not have to wait much longer to go in front after being gifted the opener on nine minutes following staggeringly casual play by Joel.
The Wigan keeper exchanged passes inside his own penalty area with Maynor Figueroa before his almost nonchalant clearance was charged down by Bale and the ball flew into the net.
But Wigan were level within two minutes when McManaman's corner was headed powerfully inside an unguarded post by Boyce.
The Latics then lost Figueroa to injury before Spurs were forced to replace Mousa Dembele as chances proved to be scarce, with Bale heading over at the far post.
A minute before half-time, Joel went some way to redeeming himself when he halted the run of Jermain Defoe in the box and also stopped Scott Parker on the follow-up.
Wigan went ahead in stunning fashion four minutes after the interval when McManaman took a touch on the edge of the penalty area before unleashing a swerving volley beyond Hugo Lloris.
Jordi Gomez, who was booked for a poor challenge on Huddlestone in the first half, then escaped further censure when his high boot caught Spurs substitute Lewis Holtby on the shoulder on the follow-through.
Roberto Martinez's side looked the most likely to score again as Arouna Kone was denied by Lloris' legs and substitute Franco Di Santo curled wide.
But, having created nothing for the entire second half, Spurs drew level when Huddlestone's low free-kick into the six-yard box was deflected past Joel by the luckless Boyce.
There was still time for Spurs to come close to snatching a winner when Joel needlessly parried Bale's free-kick before reacting smartly to push out Huddlestone's follow-up to ensure the game finished in a draw which does little to help either team.