The Dutchman was on the outside when Kimi Raikkonen and Valtteri Bottas collided heading into Turn 1, with the Ferrari driver bouncing off the Mercedes and into Verstappen's Red Bull auto, eliminating both with suspension damage.
The race turned static during a period of virtual safety auto, with cars forced to lap at controlled speeds while a Stoffel Vandoorne's crashed McLaren was cleared away.
Ferrari were somewhat caught on the hop, and when they reacted to Hamilton's stop they put the slower medium compound on Vettel's vehicle.
Asked later about his breathlessness in the vehicle, Hamilton said it was proof how physical these (2017) cars are to drive.
He added: "I don't think it's impossible to catch the leaders at some point, maybe it will take a little longer than we had hoped but we will get there".
After his win at the Spanish Grand Prix, Hamilton was asked about the physical challenges of driving in the new Formula One cars and he said it depends on what kind of race you have.
"The last stint, 25 laps, when they told me they [the tyres] had to do that I didn't think.I thought at the end of the stint he would come back but we managed it."
Raikkonen was sent on a collision course with Verstappen's Red Bull on the outside after contact with the Mercedes, with both cars suffering race-stopping suspension damage.
"Shame for the end result, but we leave Spain knowing that we can count on a auto that is solid and very quick", Arrivabene said.
"I felt like I ran out of road but I was alongside (when Vettel exited the pits)".
So on the edge is Mercedes, and so close is the fight with Ferrari, that Hamilton has elected to sacrifice having drinks during the race to help save a bit more weight.
After Hamilton overtook Vettel, he set about extending his gap to avoid the threat of Vettel coming back at him at the end of the race.
"I was feeling good and I wasn't thinking about the engine at all", he said. I tried to go around the outside as there was plenty of room there.
Next up is one of the crown jewels of the F1 circuit, the Monaco Grand Prix, in two weeks.
He then had to pressure Vettel hard for the next seven laps before getting close enough to try for a pass at the start of lap 44, sweeping past Vettel around the outside into Turn One.
"It's been a really good weekend and a great way to bounce back from Russian Federation", said Hamilton. "But at the same point you have to respect if other people do a good job and drove a good race".
The Force India duo of Sergio Pérez and Esteban Ocon were fourth and fifth, Nico Hülkenberg took his Renault to sixth, then came Carlos Sainz (Toro Rosso), Pascal Wehrlein in the Sauber-Ferrari, Daniil Kvyat (Toro Rosso) and Romain Grosjean in the Haas.