Kilmarnock manager Neil McCann told BBC Scotland: "There's a lot to like. I'm so proud of the players. We've had two weeks to dwell on the Falkirk result.
"The message was to play with risk and bravery, but that we would have to match Hearts.
"We knew they would throw balls in the box and be physical, but to a man we were outstanding and thoroughly deserved the three points.
"We did all the stuff off the ball so well. Derek [McInnes] is a first-class manager and we had to adjust our tactics to respect how Hearts would play.
"We had everything tonight and could have scored more as well. We tried to stay composed, they stuck their chests out and deserve their victory.
"The bar was set when we came in - what we expect as a coaching team. What we're doing at home is so pleasing. I want it to become a fortress."
Hearts head coach Derek McInnes told BBC Scotland: "It wasn't good enough. I didn't think we started the game well, for whatever reason. We had a good week's work going into this game.
"I thought we had a good warm-up, looked sharp and ready then and when you come away from home against a team fighting for their lives you know what to expect.
"I didn't think we looked sharp enough to the pitch of the ball, didn't close spaces down or stop crosses. I just though we looked easy to play against.
"They get far too simplistic a goal and there's no pressure on the cross and they have a free man in the box.
"We gave Kilmarnock something to cling on to and you have to credit them.
"We had 60% possession and more chances but we never really… we huffed and puffed and had a few chances but you have to say Kilmarnock scrapped and fought for the three points.
"We tried to throw more attacking players on it but it petered out. We're disappointed not with our effort but the quality of our play.
"I've told the players we still wake up tomorrow top of the league with eight games to go. We pick ourselves up and go again."