Back at the circuit where he has won a record eight times, the seven-time champion finished third for Mercedes, surviving a collision with Red Bull's three-time champion Max Verstappen in the closing stages.
"Big, big thanks to this amazing crowd and a huge congratulations to the McLarens with the one-two," he said after coming home behind McLaren team-mates Oscar Piastri and team-mate Lando Norris.
"That's my old original family so it's great to see!
"For us, the team have done a great job at pushing this car but ultimately, we didn't have the pace of the McLarens or of the Red Bulls.
"We were just able to hold on at the beginning of the race and then it was very tough to hold on and make those tyres last.
"The close battle we had at the end (with Verstappen) was a bit hair-raising but that's motor racing.
"I’m really happy and grateful for the points. A big thank you to the team," the 39-year-old added.
His Mercedes team-mate George Russell finished eighth after starting 17th as the team missed out on a chance to complete a hat-trick of wins.
Hamilton, 39, who will move to Ferrari next year to replace Carlos Sainz, moved up to sixth in the drivers' title race, with 125 points, one ahead of Red Bull's struggling Sergio Perez, who finished seventh.
Russell is eighth on 116.
Verstappen, who has now gone three races without a win, finished fifth and now leads the title race by 76 points ahead of Norris.
Verstappen has 265 and Norris has 189.
In the constructors' championship, Red Bull lead with 389 ahead of McLaren on 338 and Ferrari on 322. Mercedes are fourth on 241.
