Manager Daniel Stendel says he is "very proud" of his Hearts team for coping with the pressure of beating Hibernian to move off the bottom of the Scottish Premiership.
Second-half goals by Sean Clare, Oliver Bozanic and Conor Washington put Hearts 3-0 up before Melker Hallberg netted.
The win lifts the Tynecastle side off the bottom of the division, a point above Hamilton Academical.
"It is a great result; we deserved it," Stendel told BBC Scotland.
"We are under pressure at the moment, but how solid the players were was great."
Following Saturday's Scottish Cup quarter-final win over Rangers, the derby victory means Hearts have earned back-to-back wins over top-flight opposition for the first time in over a year.
With a home fixture with out-out-form Motherwell to come, Stendel emphasised the importance of his team replicating their last two performances.
"What's important for is that after the victory on Saturday, we did it again," the German added. "We have our next chance on Saturday at Tynecastle and we want to use all our chances at the moment."
However, for Hibernian head coach Jack Ross, it was a hurtful evening as his side's recent fine form evaporated.
The loss damages the Leith club's Europa League aspirations, as they missed the chance to narrow the gap on third place to two points.
"You can't down play the soreness of losing a game like this," Ross said. "It means an awful lot to people that come to watch the club and people that are associated with the club.
"It hurts and it stings but in terms of the bigger picture it's very easy to get caught up in the extremes of the emotion in football. That's what we've got to make sure we don't do."