Toto Wolff believes his side are back in business
Hamilton cruised to victory to move 17 points clear of Sebastian Vettel in the Championship race.
And Bottas stayed ahead of Max Verstappen, who earned his first podium of the season.
It moves Mercedes 27 points clear of Ferrari in the Constructors Championship and Wolff thinks his side are back in business.
The team chief though stressed the weekend wasn’t quite as easy as Hamilton made the race look.
Wolff said: “It wasn’t as comfortable as it looked because the race was good, Friday and Saturday were more difficult, and on Valtteri we were taking the tyres pretty far. We had pick up and a flatspot which caused vibrations which looked a bit grim. But Lewis at the front was really outstanding.
“We could see track position was so crucial. When Lewis was coming behind Max, he had the newer tyre but it’s just so difficult to overtake here.
Lewis Hamilton moved 17 points clear at the top of the drivers table
It feels like we are back in business. But let’s wait for Monaco as it’s a different ball game
“Sebastian’s front left was really bad, they needed to pit [the first time] and we were a bit worried that structurally we could have a failure so we decided to pit Lewis as well. In hindsight, we’d have rather stayed out but a structural failure ruins your race.
“I’m always on the worrying side. We’ve been very good in winter testing here and when we went to Australia everyone said it would be an easy Mercedes win and then we had difficult races. I think we were very good today but we need to stay calm and humble.
“Monaco could be a very different story. It is a track we have suffered a lot at in the past.
“It feels like we are back in business. But let’s wait for Monaco as it’s a different ball game.”
Valtteri Bottas earned his first podium of the season in Spain
And Hamilton paid tribute to his team after winning back-to-back races.
“I couldn’t have done it without this incredible team,” Hamilton said.
“These guys have done an amazing job and I’m just really proud of everyone.
“Today the car and myself, I felt that synergy which I hadn’t been feeling for the whole year. It’s a good feeling.
“This is when we’re going to start trying to continue to apply the pressure. A one-two for the team. I hope we can continue.”