The seven-time world champion passed longtime leader Lando Norris late. Norris – who was aiming for a first Grand Prix victory and leading most of the race – spun his McLaren in the pouring rain.
In addition to winning his 100th Grand Prix and becoming the first driver to achieve the feat, he returned to the top of the drivers’ championship ahead of Verstappen.
Hamilton – who overtook F1 legend Michael Schumacher for the most race wins last year – thanked his team for helping him get there.
“So it’s good to see us united again and obviously the team made an excellent call at the end,” he added.
“I didn’t want to let Lando go and of course I didn’t know what the weather was like, but I’m incredibly grateful to all these men and women who are here and back at the factory because, wow, 100.”
Take (the) advantage
While it was Hamilton who finished on the top step of the podium on Sunday, it was another Briton who seemed destined to create his own piece of history.
Norris, 21, won the first pole position of his career on Saturday, battling tough conditions to lead the field.
And after briefly losing the lead in the race to Carlos Sainz, he recovered it impressively on lap 13.
While conditions were dry at the start of the race, a downpour in Sochi made conditions difficult for the drivers.
Norris and Hamilton initially stayed on the sidelines, until with four laps to go, the Mercedes driver was advised by his team to switch to intermediate tires.
On slick tires with the rain falling harder, Norris was comfortably caught by Hamilton as the 36-year-old took the lead late.
The McLaren driver lost speed as he attempted to navigate the conditions, before losing control and spinning his car on lap 51.
He eventually finished seventh and was clearly emotional afterwards.
“I’m miserable, devastated in a way,” he said after the race. “It was my decision, I thought it was the way to go.”
“He had an amazing pace, he does a great job for McLaren, and it was obviously very bittersweet to see my old team ahead – they are doing so well, they obviously won the last race – they are doing fantastic. “