Wigan, also chasing promotion, took the lead through Ivan Ramis' powerful header after 37 minutes, but the Foxes replied four minutes before the break through Andy King.
Rob Kiernan looked to have won it for the Latics on 62 minutes, but Hammond headed in with three minutes remaining to extend Leicester's unbeaten run in the Championship to 20 games.
The Foxes will now have their automatic promotion confirmed if they beat Sheffield Wednesday at home on Friday night and QPR fail to beat Bournemouth on Saturday.
Leicester began confidently and almost went ahead in the third minute when Liam Moore's header across goal from an Anthony Knockaert cross from the left was cleared off the line by Ramis.
Wigan's first effort came in the eighth minute when Jordi Gomez curled a left-footed shot just over the bar from Stephen Crainey's cut-back just inside the area.
Leicester threatened again in the 10th minute when Paul Konchesky put in a dangerous low cross that fell to David Nugent, who shot straight at Ali Al-Habsi.
Immediately Wigan broke away and a curling cross from Gomez was met by the head of Nicky Maynard inside the box, whose effort was tipped over by Kasper Schmeichel.
Half the DW stadium thought the Latics had opened the scoring in the 20th minute when Powell won the ball 30 yards from the Leicester goal and fed Maynard, but the striker fired into the side-netting and not the net as some fans first presumed.
Wigan's persistence finally paid off in the 37th minute when Gomez floated in an inviting free-kick from the left that Ramis powerfully headed past Schmeichel from 10 yards.
The home side's lead lasted less than four minutes as Nugent played a pass to the feet of King inside the box, who turned and calmly slotted the ball past Al-Habsi via the post.
Leicester ended the half strongly, with Konchesky unleashing a fierce 25-yard drive and forcing Al-Habsi to tip it wide in the final minute of the half.
Schmeichel pulled off a fine save just past the hour to tip over a ferocious 20-yard drive from James McArthur.
But the Latics struck from the resulting corner, with Kiernan heading in another quality delivery from Gomez for his first ever professional goal.
The Foxes were not to be denied though, and equalised in the 87th minute when Hammond got on the end of a Riyad Mahrez free-kick from the right to nod past Al-Habsi from 10 yards.