Hamilton was never challenged on the way to his 41st win from pole position, surpassing a record he shared with seven-time world champion Michael Schumacher.
Hamilton should have kick-started his season with a victory at the opening rubber in Australia before a strategy mix-up by his Mercedes team gifted Vettel the win.
"I was comfortable and at no point did I feel like I was going to lose it, but I was pushing every single lap using it as a test bench to understand what I liked about the balance and how can I play with it more and how can I squeeze more out of it and do all sorts to understand what more I can get from". "We have the Mercedes board with us, it's great to have them here, for them to see that force in the team - the strength and depth". "Race by race, we can understand the tyres more, which is a battle for everyone".
"I said that I wanted to win in the way that I won and I guess, when I was coming across the line, I was just happy that I did it as I planned". But inside the auto, we were going through the tyres too quick and therefore we were not able to stay out for another 23 laps.
"Even in the end, with the fresher set, I wasn't able to attack", he added.
"Second, I think we struggled a bit over the course of the weekend with the tyres".
Red Bull's Max Verstappen celebrates on the podium with his trophy after finishing in third place.
Most improved: Mercedes may have broken Ferrari's run of consecutive pole positions, but Alonso qualifying eighth is arguably the most obvious change from previous rounds. They changed but they changed for everyone. Kimi [Raikkonen] had an issue with the engine [on Friday], had to change the engine and obviously then retired in the race. This was the second time in the last five races that only one Ferrari vehicle reached the finish line.
Vettel was called in for a second stop under the virtual safety auto as Ferrari looked to make gains with the rest of the field speed-restricted. "Hopefully, we can just work from here and score a lot of good results".
"It felt good. It was the closest I've been to feeling it is all going right, but there are still things that are not quite ideal".
The leading cars navigated the opening metres without drama before the error-prone Romain Grosjean, once labelled a "first-lap nutcase" by Mark Webber, lived up to that title by sparking a huge crash after he lost control of his Haas at Turn 3 and slid back across the track in a cloud of tyre smoke.
The 2018 Spanish Grand Prix saw a Mercedes power unit fail too - something we don't hear too often.
Vettel had pitted when the virtual safety auto was deployed to slow the field, something that had played in his favour at previous races. Carlos Sainz Jr (Renault), 8. Sergio Perez took ninth in his Force India, and Sauber finished with one point, courtesy of Charles LeClerc in 10th.