Rio 2016: Henderson wins gold after controversy
The American's sixth and final effort of 8.38 metres - a season's best – led him to a slender victory ahead of South African Luvo Manyonga (8.37m) and British defending champion Greg Rutherford (8.29m).
But the finish at the Olympic Stadium was full of controversy after Jarrion Lawson pushed for a top-three result.
The American's last jump appeared to be a good one before resulting in 7.78m – his worst legal effort – much to his disbelief.
Replays showed Lawson's left hand was grounded as he landed, leaving him in fourth. He protested with officials before accepting his fate.
Lawson subsequently tweeted: "That was a great competition. I honestly don't feel like I lost. Of course I don't think my hand hit the sand, but Greater is ahead!"