The Jambos, who made their first inroads into their 15-point season deficit, beat Hibs 1-0 at Tynecastle thanks to a 72nd minute winner from Callum Paterson.
The win made it nine from the past 16 outings between the clubs in all competitions, with Hearts losing on just two occasions during that time, and manager Gary Locke was delighted with how his players performed.
"It's a huge, huge win,” he said after the match.
"It did not matter who we were playing, getting the first win and putting a wee bit of pressure on the teams above us was huge and it helps against your biggest rivals as well.
"The fans have been through a lot over the summer and hopefully that will be a result that keeps them happy tonight.
"It gives everyone at the club a lift, I was not too disappointed when we lost last week and I'm not going to get too carried away today.
"The sooner you get a win with the situation we're in, the better. We've done that and now we have something to build on.
"It certainly was not a classic but you saw two teams that were competitive and one wee bit of quality has won us the game."