Starting third, the Mercedes driver seized the opportunity of front row starter Charles Leclerc losing momentum out of Turn 1, following a failed move past Verstappen away from the start, to grab second place.
But although Hamilton was then able to shadow Verstappen for the opening laps of the race, eventually he fell out of DRS range before coming home 9.4 seconds behind.
While Hamilton felt that upgrades at Mercedes had helped his team make a step forward this weekend, he said the form shown on Saturday highlighted how much of an edge Red Bull still had.
“That was a fun race,” he said. “Good start down to turn one, and good battle with Charles.
“Then I was trying early on to get closer to Max. But their pace is just undeniable at the moment.
“I'm happy we're a little bit closer. We’ve still got a long way to be able to eke the pace that he was doing throughout the race. But nonetheless, I'm really happy to be back on the podium.”
Hamilton’s hopes of doing better in the grand prix on Sunday will be boosted by the fact that Verstappen is starting in sixth place, but he was in no doubt that the Dutchman would be a threat for the win.
“Ultimately, I think he will be breathing down our necks before too long, with the pace that he had today,” he said.
“But I think that will open up for a good fight with Charles and Lando. We're all quite similar in pace. So hopefully, we get to have a good battle tomorrow.
“And if we can all keep Max behind. that'd be awesome. But if not, no worries.”
Verstappen himself said that he never felt particularly threatened in the race after he shut the door on Leclerc at the start, despite Hamilton being within DRS range early on.
“It was always like eight/nine tenths for a few laps, but that was all controllable into the braking zone,” he said.
“The DRS, with such big wings here on this track, they're quite powerful. But once I cleared the DRS, then, yeah, we all settled in our own rhythms. And I think the pace of the car was very good today.”