The 2-0 win at Tynecastle means that Hearts will go into their final game of the season at Kilmarnock just one point behind third-palced Aberdeen who entertain Rangers next weekend.
"It's a massive victory," the Hearts coach told BBC Sport.
"We've given ourselves a chance of European football now.
"We were under a lot of pressure to win. Derby games are always important to the fans and the players.
"The first half performance was very pleasing. We were probably hanging on a bit as Hibs put us under pressure but it's a fantastic three points."