The Gorgie club have been struggling at the bottom of the Scottish Premiership after being deducted 15 points and banned from signing players having fallen into administration.
However, Gary Locke's young side had won both meetings between the two Edinburgh sides this season.
In an exhilarating third clash, Hibs striker James Collins put the home side ahead in the 59th minute before Jambos substitute David Smith, on for Callum Tapping, drew the visitors level in the 70th minute.
However, with nine minutes remaining Hearts defender Jordan McGhee was adjudged by referee Bobby Madden to have fouled Lewis Stevenson in the box with Craig slotting in the spot-kick.
The former St Johnstone midfielder said: "That goal is up there with the biggest of my career so far.
"I've scored ones in the past that have helped clubs get into Europe or the top six.
"But to score a winner in the derby - it doesn't get much better than that.
"We've been unfortunate to lose the last two games against Hearts.
"To be fair to them, they've got a goal, sat in and weathered whatever we've thrown at them.
"As players, we look at the bigger picture, kicking on up the league.
"We're in the top six now and it's about pushing on.
"But, as a fan, you want to win the derby games. We've not won a lot lately so they'll be delighted.
"They'll have the bragging rights for the next few days."
While Jambos boss Gary Locke did not think Hibs should have been awarded a spot-kick, stand-in captain Ryan Stevenson admitted: "If it was us I'd be saying it was a penalty."
However, the Tynecastle forward insists McGhee, a late replacement for Gorgie skipper Danny Wilson, who was ill, will be spared any recriminations.
"It's just a silly mistake, one that's cost us, but nobody will be giving him a hard time," said Stevenson.
"It's just inexperience from Jordan. You need to keep in mind, he has just turned 17.
"To be playing in a game of this magnitude, with everything that surrounds the derby, says a lot for him.
"He is a boy with a massive future in the game.
"He was sitting in the dressing room absolutely devastated.
"He knows he's made a mistake, everyone makes mistakes, but as an older player I know what he's going through so I'll be the first one to get him back up.
"He just needs to put this to the back of his mind because none of us can feel sorry for ourselves."