The reigning champions switched the group of engineers and mechanics around at the end of last year, with most of those who had worked with the Briton now assisting his German team mate Nico Rosberg.
With Rosberg winning the first four races of the season to build a substantial lead in the championship, Mercedes have already had to deny conspiracy theories and the pressure was building.
Sunday's race, with Hamilton making the right strategy call and clearly faster than Rosberg, who was asked to move aside after struggling to get the tyres up to temperature, was the Briton's first success of the season.
"Hopefully it will be a boost for my mechanics who have been nervous all year," Hamilton told reporters. "It's not easy coming from one side of the garage (Rosberg's) to the world champion's car.
"Because of the issues we've had, they probably felt like 'we're not delivering' but they have been delivering. Today must be a great relief for them and I am grateful for them for sticking through it, sticking with me.
"Hopefully today will give them the confidence to know that I am just as strong as I've always been and I will be for the rest of the year."
Hamilton had been 43 points behind Rosberg before Monaco, the showcase race that every driver wants to win, but ended the weekend only 24 adrift and with everything to play for.
With 25 points for a win, and 15 rounds remaining, the Briton now heads to one of his favourite races in Canada with high hopes of reducing the deficit further.
Despite Sunday's unexpected bonus, Hamilton said Mercedes were under more pressure than ever.
Red Bull triumphed in Spain, 18-year-old Dutch driver Max Verstappen becoming the sport's youngest winner, and were favourites to win again in Monaco before a calamitous pitstop cost Australian Daniel Ricciardo first place.
Ferrari, off the podium in Monaco, are also hoping to come back much stronger in Montreal in what is shaping up as a three-way battle despite Mercedes winning five of six races.
"There are still issues, mistakes are being made," Hamilton added.
"You are starting to see some more buckles here and there. What is really important is that we pull together... we need to refine a few areas."; Editing by John O'Brien
(Editing by John O'Brien)
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