Coming off four straight titles in both the constructors' and drivers' championships, Mercedes had started the season by showing good pace in Australia, although it let victory escape thanks in part to an ill-timed safety auto that helped Ferrari's Sebastian Vettel earn the win in Melbourne.
"This is more like it", Hamilton said on the team radio.
Lewis Hamilton is out of contract with Mercedes at the end of the season despite talks of a new deal being ongoing since the end of a year ago.
Hamilton is now standing at the top spot in the drivers' championship, maintaining a lead of just four points over Vettel.
"Honestly I think Monaco is going to be hard for us", he said after Sunday's race.
While the top three in qualifying were separated by barely a tenth of a second and the rest of the leading six also set a hot pace, the gap beyond was vast.
"I only said that we are loyal first of all to our drivers. The first run was not so good, but the last lap I was happy", he said. I think I've been able to really continue good performance since the very end of a year ago. He has some serious records. But once the Safety Car pulled in at the end of lap six, Hamilton was in a race nearly on his own, a rapid first stint suggested that there was one man in contention for the win. "It's hard to beat all of these records that he has".
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"But [I have] the will to want to get this one and do it right, ideal weekend in, weekend out".
"So that's why I'm only partly celebrating", he added.
Hamilton had also won in Azerbaijan two weeks ago, but that victory came mostly because of incidents involving his closest competitors, including a blown tyre for Bottas, a mistake by Vettel and a crash between Red Bull teammates Daniel Ricciardo and Verstappen.
The Haas F1 Team has started 2018 with a cracking little vehicle, as demonstrated by Kevin Magnussen who finished sixth in Barcelona. Sergio Perez finished in ninth place ahead of the Sauber of Charles Leclerc.
Vettel won the Monaco race previous year, when Ferrari was 1-2 in qualifying and in the GP.
Hamilton had a clean start, with Vettel moving from third to second by passing Bottas on the outside of Turn 1.
By contrast, the track at Barcelona is much better suited to the W09 - as today's dominant performance from Lewis Hamilton demonstrated. "People probably think it was an easy race, that I was cruising".
"Apparently, the changes that were made did us more harm than it did our opponents", Ferrari's Vettel said.