The leading cars navigated the opening metres without drama, but the same could not be said further behind after a three-way crash was sparked by the error-prone Romain Grosjean.
"I think today has been a rejuvenating experience", Hamilton told reporters.
"I've been racing a long time so to still have that feeling when you do have that win, and that happiness and that uplift inside (is special)", he said.
"I am much happier with the vehicle".
Vettel got off to a great start this season, winning the first two races, before his fortunes changed for the worse.
Vettel has now had to settle for a disappointing fourth place in two successive races and has lost signficant ground in the championship battle with Hamilton.
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"It was very close but I am very happy", Hamilton said.
"I know they went softer but.the working range is far narrower than it was previous year". Was this a case of Ferrari's strategy going all wrong? "So I hope we can continue".
"We couldn't make the tyres last, so for us it was clear we come in again".
"We were going through the tyres quicker than the others today".
The lack of performance from Ferrari would be alarming. Ultimately Vettel lost out to pole by under 0.2 seconds. On the mediums, his Ferrari could manage only half of the number of laps (24) as Bottas (47).
The other issue for Ferrari was their unreliability.
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Ferrari's day went from bad to worse when Kimi Raikkonen suffered an issue with the vehicle and pulled over. The rain threatened to return, with clouds hanging darker than the Catalan tarmac, and with the four race strong streak of safety cars both virtual and real, a monkey wrench looked certain to be thrown into the race's proceedings. The speed is there and the driveability is much better than Mercedes' auto.
That error meant the German emerged back on track behind Verstappen's Red Bull. Ricciardo was eventually called in on lap 34, with Verstappen pitting a lap later.
In securing his second win of the 2018 campaign and his first back-to-back triumphs following his win in Baku, Hamilton proved that Azerbaijan wasn't just a flash in the pan, even if it could have been described an "inherited win". "Hopefully, we can just work from here and score a lot of good results".
Australian Daniel Ricciardo was fifth in the second Red Bull ahead of Dane Kevin Magnussen of Haas and Spaniards Carlos Sainz, of Renault, and two-time champion Fernando Alonso, of McLaren. It was only revealed post-race that one of the reasons for this huge gap was a spin after the Virtual Safety Car restart on cold tyres. Grosjean was punished with a three-place grid penalty for the next round in Monaco.
Hamilton held his lead from lights out but Vettel made up a place on the drag race down to turn one passing Bottas for second.
As a result, his auto created a cloud of black smoke and was invisible to following drivers as they raced into it - Nico Hulkenberg, of Renault, and Pierre Gasly, of Toro Rosso - both smashing into him.
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