In an enthralling Scottish Premiership encounter, Hibs striker James Collins put the home side ahead in the 59th minute when he lashed the ball high into the net from four yards after the Tynecastle men failed to deal with a Craig corner.
Jambos substitute David Smith, on for Callum Tapping after the break, drew the visitors level in the 70th minute but with nine minutes remaining Hearts defender Jordan McGhee was adjudged by referee Bobby Madden to have fouled Lewis Stevenson in the box.
Craig stepped up to score from the spot and give Butcher his first Edinburgh derby win since taking over as boss at the end of last year and with that, the former Motherwell manager pointed to Hibs fan Murray's exploits when he won the men's singles title for the first time.
"It feels terrific," said the Englishman. "It is a lovely feeling because the club, the players and fans have suffered a lot this season from Hearts.
"Tonight was all about winning the match.
"I said to the players before the game, it is very much like Andy Murray when he went out for the men's singles final at Wimbledon with the whole nation on his shoulders.
"He just thinks about it as a tennis match. All our players were thinking about today is that it was a football match and best get on with it.
"You've seen that Andy collapsed at the end of it when he won, it hit him then.
"I said to the players that is what I wanted, them to have that impact of winning the match.
"I was delighted with the reaction of the players when they did concede the goal.
"In the past maybe Hearts would have got a point or won the game but we dominated again and I think we deserved to win the game."
Asked about the penalty, Butcher said: "I think it was the right decision, there was no need to make the challenge on Lewis, he was wiped out. Anywhere else on the pitch it was a foul."
Hearts boss Gary Locke revealed that McGhee, a late replacement for Gorgie skipper Danny Wilson, who was ill, was "distraught" at conceding the penalty, a decision queried by the former Jambos skipper.
Locke said: "Jordan feels he didn't do anything wrong. I have seen it again and he goes across the lad but the ball is already out of the pitch.
"You see that type of thing happening every week, there is never a foul given but he decided tonight to give a penalty.
"It is a sore one. I don't want an explanation from the referee.
"Some of the decisions we have had against us have been incredible and I just hope our luck turns in 2014.
"I thought we defended well and worked our socks off to get back into the game, and a controversial decision cost us a point.
"But I couldn't be more proud of the players, they gave us everything again."
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