Two penalty saves from Jamie MacDonald wasn’t enough to earn Kilmarnock a point as Hearts strengthened their grip on third place.
MacDonald had made a brilliant save to deny Jamie Walker from the spot after Stuart Findlay brought down Prince Buaben in the box, but Walker scored with the second attempt, deftly chipping the goalkeeper to give Hearts the lead.
Nicholson came close to extending the advantage but his saw header come off the post before Hearts were awarded a second penalty to kill off Killie hopes.
However, just like the first penalty MacDonald guessed the right way to push the ball onto the post this time to deny Abiola Dauda.
Hearts boss Neilson admits he knew MacDonald had it in him to hurt the Jambos. “That’s what Jamie is good at – shot-stopping. I spoke to the players before and I said, ‘If we get a penalty, get in for that second ball because we know he is very good at that, that’s his forte’.
“Anything around about him, he will save it.
“He has saved two penalties at Tynecastle and there won’t be too many people who have done that.
“If we had got the second goal it would have killed the game. But it got more difficult and then I thought we defended well.”
Hearts survived a late scare after a goalmouth scramble nearly presented Greg Kiltie the chance to snatch an equaliser but the Jambos held on.
Robbie Neilson’s men are now 11 points clear of fourth in third place while Kilmarnock will be looking over their shoulders as the gap narrowed to eight points with United a game in hand.
But Lee Clark is confident they have enough quality to get out of the relegation scrap.
He said: “We can only affect our own results, but there is definitely enough here and we just have to believe we have got enough. I do and the staff do, and we’ve got to keep ploughing on.”