Hamilton was more than half a second slower than Bottas in qualifying and as the Finn made a blistering start from third and took the lead at the first corner, Hamilton did not make ground from fourth on the grid.
The 32-year-old suffered overheating problems as he chased Raikkonen in the first stint of the race and dropped back over the pit-stop period to finish 25 seconds behind the Finn and 36 behind Bottas.
"I don't remember the last time we had that [overheating]," Hamilton said. "It meant I was out of the race from the get-go.
"I think I had the pace to fight with Kimi but the car was just overheating the whole the time. I'm sure we will go back to the drawing board and figure it out."
I can fight for the title - Bottas
Bottas joined Mercedes over the winter following the retirement of world champion Nico Rosberg.
Bottas said his first win felt "surreal", but added: "It's a good feeling and I am happy."
He added: "I always knew I could get good results if everything goes right and I always trust in my ability. But it's nice to get confirmation that the results are possible.
"It took quite a while, more than 80 races for me, but it's definitely worth the wait. This strange opportunity came to me in the winter to join the team and they made it possible, so I want to thank them."
Bottas moves into third place in the championship, 23 points behind Vettel and 10 behind Hamilton.
He said: "[Winning the title] has always been the only goal for me in my career but I have not had the chance to prove it. Now I have the chance to prove I can win races and titles. Two weeks ago people were saying I am the number two driver but today it looks very different."