The team's third one-two finish in four races this season left Verstappen six points clear of the Mexican in a two-horse title battle.
The Dutch driver started on the front row in Baku, taking the lead from Ferrari's Charles Leclerc on lap four but pitting just before the safety car was deployed.
Perez, yet to pit and able to do so without losing position, made the most of his good fortune.
Verstappen said he had been experimenting all race with steering wheel settings, looking for a better balance in the car.
"I actually think that I found a good compromise towards the end of the race because I think my last 10 laps were a lot stronger. And I felt a lot happier with the car, how everything was behaving," he told reporters.
"So I think all in all, I can be quite pleased with second," added last year's race winner.
"I mean, of course, you always want to win, right? But I think sometimes you need these kinds of weekends to learn and have a better understanding of the car, of what the car needs to go faster.
"And sometimes on the street circuit like this, it really comes out. Sometimes these kinds of things might get a bit masked on a normal track because of downforce and just the general behaviour of a car.
"So, maybe this was a good day, you know, to go forward."
Third was best Ferrari could do, says Leclerc
Ferrari are still too slow to win and third place behind the Red Bulls in Sunday's Azerbaijan Grand Prix was the best they could have hoped for, Leclerc said after securing his team's first podium appearance of the Formula One season.
Leclerc started from pole position, and had finished second in the Saturday sprint from the same grid slot, but was unable to stay ahead for more than three laps.
"That was the absolute maximum I could do today, or that we could do as a team," said the Monegasque, who finished 21 seconds behind race winner Perez in what he said was his "loneliest ever" race.
"(The) strategy was really good, everything was really good but we just don't have enough pace in the car today to fight with the Red Bulls.
"And also Aston Martin seems to have a stronger race car than we do. It was a good effort to stay in front of Fernando (Alonso) but at the end it's like this. The reality is we have a lot of work to do to be back for the win."
Leclerc had arrived in Baku with a meagre six points from the first three races, thanks to two retirements, but he left with a total tally of 28. Spanish teammate Carlos Sainz finished fifth.
Ferrari have upgrades in the pipeline, planned for their home race at Imola in May, but Leclerc said he was expecting small steps rather than miracles.
Team boss Fred Vasseur said the weekend had been a morale boost for the team.
"For the motivation it was important," said the Frenchman. "You have to take the positive of the weekend. I think on one lap (qualifying) the pace was there and now we have to improve a bit on the long stint."