"This is just what the doctor ordered," the Austrian told reporters.
"We needed that win, he needed that win."
After going eight Formula One races without success, a run dating back to Texas in October where he clinched his third championship, the most glamorous grand prix on the calendar provided what Hamilton was looking for.
The Briton had suffered power unit problems in two of the previous five races and collided with German team mate and championship leader Nico Rosberg at the start in Spain two weeks ago.
On Saturday, he had qualified third after fuel pressure problems threatened an even greater handicap but his fortunes changed in the race.
"It's just a big relief that we were able to score that win with him after such a terrible streak of bad luck," said Wolff.
Hamilton recognised he had been through a tough time.
"When you keep falling it’s hard to always come up with innovative ways to keep yourself motivated...to keep believing," he said.
One man with plenty of belief was Canadian singer Justin Bieber, who got the party rolling by turning up at the finish to congratulate the winner.
Hamilton handed him the bottle of fizz, before taking it back and showering team mechanics and marshals. The historic trophy, won by so many of the greats and presented by Prince Albert, was tossed in the air.
The win was his 44th -- a special number to the Briton through his racing career and also the one he has on his car.
"I’m massively overwhelmed," said Hamilton of his second victory in Monaco, the first coming with McLaren in 2008, that cut Rosberg's lead to 24 points.
"It’s been a long time coming to get this win, not only in this season but to get the grand prix win here. This is one the toughest, if not the toughest, races of the year for us."
If he had cut a glum figure on Saturday evening, after qualifying third, Hamilton said the mood soon passed and he relaxed with friends, even enjoying a beer. Sunday night was likely to see a few more.
"I am sitting here and everything is quiet, and a bit dull, not particularly exciting, but when I leave here it is going to be super exciting. I am going to be having fun," he said.
(Editing by Ed Osmond)
