The Edinburgh outfit have been gradually clawing back the deficit - handed down for entering administration - since the start of the season, but have now reached positive figures after 24 matches.
Callum Paterson netted the opener with a left-footed effort in the 37th minute, before Yann Songo'o levelled matters on the stroke of half-time.
Scott Robinson settled the encounter, firing home from the centre of the penalty area in the 80th minute to seal Hearts' first win in 12 matches.
At the top end of the table, Aberdeen held Motherwell to a 2-2 draw - a result that will play into the hands of leaders Celtic, who play on Sunday.
But that joy was shortlived as Motherwell retook the lead through Zaine Francis-Angol's strike from close range two minutes later.
