The Dutchman made a blistering start where he climbed 10 places in the opening three laps.
Both Red Bulls were forced to start from the back of the field after incurring engine penalties for improved power supplies.
Verstappen started on the soft tyres – the most durable available – and he found himself leading the race for over 30 laps with a late pit strategy.
While Verstappen was out front Hamilton had a couple of attempts to leapfrog the birthday-boy, who turned 21 today, but the Brit failed to get past.
Hamilton finally got past when Vertsappen pitted but the Red Bull driver can take solace from his showing and hopes to build on that at the Japanese Grand Prix next weekend.
“We need to wait and see because there is a straight without any DRS, which makes it extra painful for us,” Verstappen said.
“Even today you saw that when Lewis got close he wasn’t able to attack, so everything will depend on qualifying, but we will see.
“The car was in any case great again this weekend.”
Verstappen’s late pit meant he had the fresher tyres later in the race but he chose not to attack fourth-placed Kimi Raikkonen to save his eying for the final five races of the campaign.
“It went well. The target had always been to finish fifth, but we can be very satisfied the way we achieved that today,” Verstappen added.
“I had a decent start and was able to move through the traffic and before long I was fifth, so that was very good.
“My car felt good and the grip was also immediately there, so we were able to easily move up. It all felt good, so I am very happy with that.
“We had to bring the car home and there wasn’t much more in store. Just no chance. The left front tyres would be destroyed after a few laps, so you are not really able to push.”
Meanwhile, Red Bull boss Christian Horner was gutted his team had to bring Verstappen in for a tyre chance.
“It was a shame he had to make the stop really, but of course it is mandatory,” Horner told Sky about Verstappen’s opening stint,” he said.
“The other compounds were very fragile, so we stopped as late as we could, but we could see already they were starting to chunk up a little bit.
“At that point you are too far behind Kimi to have a go at him, so it was a question of we took the penalty of the engines here, let’s save these now for the races coming up.”