The early stages showed how nervous both sides were with neither team able to string two passes together.
This meant there was precious little happening happen in front of goal, although Motherwell did produce a couple of long-range efforts, from Brian Kerr and Scott McDonald, without threatening the keeper.
The best action was actually kept for the four minutes added on, with Richie Foran missing a great chance after he was put clear one on one with the goalkeeper by Marc Fitzpatrick's throughball.
At the other end Hearts saw a Neil McCann shot blocked by Stephen Craigan.
The opening stages of the second half were cagey although the game did open out in midfield allowing both sides to get into passing mode, but there was still a dearth of goalmouth action.
The stalemate ended on 69 minutes when Hearts broke after clearing a Motherwell corner. McCann moved forward quickly before releasing Mole, who rounded Colin Meldrum and eventually shot home past a posse of Well defenders on the line.
Hearts almost made it two in bizarre circumstances when a Craigan clearance inside the six-yard box ricocheted off Mole and on to the post, before bouncing into the grateful arms of keeper Meldrum.
Motherwell's best effort came when a Craigan long throw eluded the visiting defence and Keith Lasley nipped in at the front post, but his shot was too close to Craig Gordon.
Gordon sealed the win for Hearts with two minutes left when he pulled off a stunning one-handed save from Jim Paterson's close-range effort.