He also pitted for a new front wing.
The overall win in the 2017 series makes Hamilton Britain's most successful Formula One driver, lifting him above Jackie Stewart who won three titles.
Argentina's Juan Manuel Fangio sets the bar in second place with five world titles, impressively earned in just seven full seasons.
"I hated every bit of that race", said Wolff.
"It is not the kind of race I wanted, 40 seconds behind, but I never gave up", Hamilton said.
The race was won by Dutchman Max Verstappen, with Valtteri Bottas and Kimi Räikkönen making up the rest of the podium positions.
"And then of course big congrats to Mercedes, I mean really incredible job what you've done across this massive regulation change".
Caroline Wozniacki won the biggest title of her career when she beat Venus Williams 6-4, 6-4 in the WTA Finals in Singapore.
Dane Kevin Magnussen finished eighth for Haas ahead of Hamilton and two-time champion Fernando Alonso, who battled hard to resist Hamilton before finishing 10th for McLaren.
The stewards decided that no investigation was necessary.
Mercedes' non-executive director Niki Lauda, a three-time world champion, hailed Hamilton's achievement.
"I was confident the car was going to be good because, looking at the long run pace, it was very easy for us to do quick lap times", he told Sky Sports. The championship is at stake and I think in normal conditions there would have been a penalty.
The Brit moved past Prost into second in the all-time list during the 2016 season and has since gone clear of the Frenchman with nine more race wins so far this year. Zobel made a two-putt par on No. 18 to send the match to extra holes and clinched the title with a par putt on No. 1.
"And also then Lewis versus Seb has been exciting and everybody else who came in the mix from time to time".
In 1995, aged 10, and wearing a jacket and shoes borrowed from his predecessor as British Formula Cadet karting champion, he went to a glittering awards ceremony in London where he met McLaren's then-boss Ron Dennis.
"Did he hit me deliberately", asked Hamilton over the team radio.
Escaping the management regime of Dennis and his father, Hamilton found freedom at Mercedes alongside team-mate German Nico Rosberg, his teenage karting friend and rival.
There was no note of hubris in the comments of Hamilton Sr as he stood among the diggers excavating his latest construction venture, just the observation of an outsider who watches as his son commands F1 week by week to become a legend in his own racing lifetime.