Mercedes driver, who is now 48 points behind Vettel, says it has not been the easiest of months for him since break-up with pop star but looks forward to competing at his best.
Hamilton dedicates Hungarian GP win to ex-girlfriend Scherzinger
The 28 year old conjured a victory drive in Sunday's race described by Mercedes' non-executive chairman and three-times world champion Niki Lauda as the best he has seen from the Englishman.
It was Hamilton's first for Mercedes at the 10th attempt following his move from McLaren, the 22nd of his F1 career, and remarkably his fourth in seven years around the Hungaroring.
This professional success comes against the backdrop of turbulence in his personal life, following the break-up of his relationship with popstar Scherzinger, and he told several national newspapers: "It has not been the easiest few months.
"It feels a little bit odd without that someone here – but I would say now that this is one of those races you want to dedicate to that someone.
"The thought in my mind through the whole race was of someone really special to me and I want to dedicate it to her. For the next few days, this will keep me riding high. It is a bit of a Band Aid that will cover me for some time."
"I am still working on getting those puzzles [in my life] in place and there is a big part of the puzzle out of place at the moment," Hamilton added. "At some stage, maybe it will come back together."
With Sebastian Vettel third behind Kimi Raikkonen, Hamilton has now closed the gap to Red Bull's triple world champion to 48 points.
With Mercedes finally appearing to have cracked their tyre problems, Hamilton may prove to be Vettel's closest challenger after the summer break that now beckons.
Assessing his chances, Hamilton said: "When you have a win like this you get excited and think anything is possible.
"Obviously this race shows anything is possible, but it's still too early to say we can challenge.
"I know the guys are working hard to close the gap, and I hope this is the first step in doing so.
"But we've a lot of tough races coming up. I just hope that's not the last time my tyres work for me.
"If we can be quick at this track and make our tyres last with the temperatures we experienced then we should be able to do it anywhere, so fingers crossed."
Mercedes had previously proved inept at making Pirelli's rubber work for them during races, particularly in the heat.
In Sunday's race the mercury hit 35 degrees centigrade, whilst track temperatures soared to 50, and from the 30th pole Hamilton should have been a sitting duck for those behind.
But the new construction of Pirelli tyres that debuted in the race and marry last year's construction with this season's compounds appear to have had an effect.
Even so, Hamilton added: "I really wasn't expecting it [the win].
"I talked it down a lot after qualifying because I was expecting a real tough race. I thought we were going to fall behind.
"The experiences I had at McLaren were some of my greatest, but this is one of the highlights of my career up to now, one of the most important wins.
"Moving to a new team, one that was struggling massively last year, and to finally get a win with them after the first 10 races is a great feeling."
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