While Mercedes consolidated their lead in the overall Championship tally for the season, rivals Ferrari had a horrid day on the track as both Sebastian Vettel and Charles Leclerc had to pull out of the race following a collision in the first lap.
Hamilton secured his maiden win off the season after he started in front of the grid on the back of an amazing qualyfing performance where he took pole position by more than 1.2 seconds.
"The team did a fantastic job with their strategy. I'm so grateful to be back in first place. It feels like a long time coming. This is a great, great step forward. I love back to back (races)! I could do it all season long," said Hamilton after the race.
Bottas, who came second, said: "Lewis had a good start and he could control the race. For me, starting from fourth was damage limitation so to get second isn't a bad result.
"It could have been better but I'm looking forward to heading to Hungary next week," he added.
Meanwhile, Verstappen said he did try to make it difficult for Valtteri. "A podium was good, but still a lot of work to do."
Leclerc also apologised for a rash move on the first lap that took out both cars. "I am disappointed in myself. I'm sorry but being sorry is not enough. Seb (Sebastian) hasn't got any faults today.
"I've let the team down after them working a whole week to bring the updates early. Too eager to gain those places in the first lap. I will learn from it," he said in a tweet.
With the first three spots sealed in dominant fashion, an exciting battle for fourth place saw the Red Bull of Alex Albon finish ahead of the McLaren of Lando Norris, Norris passing the Racing Point of Sergio Perez with one corner to go in the race after the Mexican suffered front wing damage from contact with Albon.
Perez was classified sixth, ahead of teammate Lance Stroll in seventh and Renault's Daniel Ricciardo finished eighth.