McLaren have bounced back impressively from a worrying slump of form at Valencia and Silverstone with strong performances in Germany, where Jenson Button finished second, and at the Hungaroring.
Despite his well-judged win, which saw him fend off pressure from Lotus team-mates Romain Grosjean and Kimi Raikkonen, Hamilton remains 47 points adrift of championship leader Fernando Alonso.
In the constructors' standings McLaren have moved up to second place, 53 points adrift of Red Bull.
And, boosted by the team's 178th victory, Whitmarsh believes they are now firmly in the title picture as F1's month-long summer break gets under way.
He told the team's official website: "The 25 points Lewis has annexed here have taken his season-so-far total to 117.
"Although he's still a little way behind the drivers' world championship leader, he's now very well placed to mount an assault on the drivers' world championship crown over the remaining nine races of the season. Believe me, it's still all up for grabs.
"In the constructors' world championship, the 33 points that Lewis and Jenson scored have lifted Vodafone McLaren Mercedes to second place overall.
"Again, as with the drivers' world championship, we're in a good position from which to work as hard as is humanly possible to close the gap on the leaders and wrest the constructors' laurels by season's end.
"We'll now take our holidays, we'll recharge our batteries, and we'll return at Spa-Francorchamps in a month's time, fighting fit and ready to do battle once again."
While Hamilton took the spoils, second-placed Raikkonen's future was in the spotlight following yet another impressive drive from the Finn.
Rumours have linked the 2007 world champion with a return to Ferrari, with Felipe Massa rumoured to be on his way out, and he did not rule out the possibility.
But Lotus boss Eric Boullier is confident Raikkonen will remain with the Enstone-based operation in 2013.
He told Finnish broadcaster MTV3: "There are always a lot of rumours.
"We have a two-year contract with Kimi but, as in every agreement, there are always options.
"I believe Kimi is happy here and I do not believe that his experience with Ferrari was the best one.
"Being with (team-mate Romain) Grosjean is certainly easier than Alonso.
"I can't see why Kimi would want to be the second driver at Ferrari when he has the chance to be the number one here."
Red Bull boss Christian Horner, meanwhile, hit out at the constant questioning his team are facing over the legality of their RB8.
The team were caught up in a row over engine mapping at the Germany Grand Prix, and in Hungary it was reported that the FIA had asked the team to alter a device on their front suspension at the Canadian Grand Prix in June.
But Horner dismissed the controversies, telling reporters: "The bottom line is the results sheet comes out at the end of qualifying or the end of the race and the car complies with the regulations.
"All the rest is all bull****, at the end of the day it's all down to the FIA and the stewards to decide whether the car's legal or not.
"Every single time our car has been questioned by other teams it has always been compliant with the rules."