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.
Reza Ghoochannejhad struck a brilliant first goal in England and goalkeeper Ben Hamer saved a last-minute penalty to boost Charlton's survival bid and send Leeds crashing to a third straight defeat.
Ghoochannejhad - he has his first name Reza on the back of his shirt - curled home the only goal of the game from the corner of the penalty area early in the second half to lift Charlton three points clear of the relegation zone.
The Iran international's first goal since arriving at Charlton from Standard Liege in mid-January secured the Londoners only their fourth league win on the road this season and did little to lift the gloom at Elland Road.
But Charlton's success owed as much to Hamer, who saved superbly to deny Ross McCormack's late spot kick after Charlton midfielder Diego Poyet had shoved Aidy White in the area.
Dale Stephens scored his first Brighton goal to rescue a point in an entertaining 3-3 draw against Blackburn at Ewood Park.
Both sides were looking to strengthen their play-off hopes and David Rodriguez helped Albion draw first blood with a low finish for his first goal in Brighton colours.
Rovers rallied and Jordan Rhodes diverted a Tom Cairney free-kick home from close range before Cairney got on the scoresheet just before half-time from close range.
But Brighton fought admirably and Gordon Greer's first of the season drew them level after 78 minutes before a breathtaking final few minutes that saw Rhodes score Blackburn's third from the penalty spot before Stephens headed in soon afterwards.
It was a result that ultimately damaged both teams' play-off ambitions, with Rovers seven points behind sixth-placed Reading and Brighton three points back from the Royals.
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