Wotton rifled home a low 75th-minute shot, less than two minutes after coming on, just as it seemed as though Steve Lomas' header two minutes before the interval would secure a valuable three points for the Londoners.
Earlier, Scottish international Stevie Crawford missed a gilt-edged chance to open the scoring for Argyle after 13 minutes. David Friio slipped to allow the former Dunfermline man in but he blasted the ball wide of the target.
Argyle spurned another gift when Micky Evans seized on goalkeeper Romain Larrieu's free-kick. He was in acres of space behind the Hammers defence but when he teed the ball up for Friio, he could only produce an embarrassing air-shot.
The Pilgrims were immediately made to pay. Hayden Mullins' right-wing cross found Lomas waiting at the near post and he nodded the Hammers ahead.
In the second half, David Norris was thwarted by an excellent save from West Ham goalkeeper Stephen Bywater, who twisted to tip over a header from point-blank range by the Argyle midfielder.
Bywater was at it again a few minutes later, producing another brilliant finger-tip save to flick over Evans' header from Lee Hodges' inswinging free-kick.
It seemed that the West Ham keeper would have the last word. Then came Wotton's dramatic late intervention.