Tensions were running high between the two Edinburgh sides from the start, with Kevin McHattie earning the game's first yellow card after just five minutes for body-checking Wotherspoon.
Hearts looked the more likely to score in the opening period, with the home side struggling to get the ball to in-form striker Leigh Griffiths.
Darren Barr had a chance to give Hearts the lead early in the second half but his shot flew wide.
Hibernian had to make their first substitution after Griffith landed awkwardly having tried to win a high ball. The 22-year-old had to be stretchered off, and was replaced by Ross Caldwell.
Eoin Doyle put the ball in the back of the net shortly after the hour mark, but had the effort ruled out for offside.
Wotherspoon's 84th-minute strike put Hibs ahead, the ball taking a deflection off Hearts captain Zaliukas.
Callum Paterson had a chance for an equaliser just before the final whistle, but saw his shot go high.