The triple Formula One world champion took the chequered flag just 0.725 of a second ahead of the man who beat him at the previous round in Miami.
The win was Verstappen's fifth in seven races this season, the 59th of his career and the third time in a row at Imola. Last year's race at the Italian circuit was cancelled due to heavy flooding.
"I had no grip anymore. I was sliding a lot. I saw Lando closing in. The last 10 laps were flat out," said a relieved Verstappen, who had appeared set for another easy win but had to sweat ultimately for the spoils.
"It's difficult when the tyres were not working anymore and you have to go flat out. I couldn't afford to make too many mistakes. Luckily we didn't."
Ferrari's Charles Leclerc was third at the Italian team's atmospheric home track, 7.916 off the pace, for his fourth podium finish of the season and a home race to come in Monaco next weekend.
The victory extended Verstappen's championship lead to 48 points, with Leclerc now his closest rival after Red Bull's Sergio Perez started 11th and finished only eighth.
Verstappen has 161 points, Leclerc 113 and Perez 107. Red Bull have 268 in the constructors' standings with Ferrari on 212 and McLaren on 154.
McLaren's Oscar Piastri finished fourth with Ferrari's Carlos Sainz fifth and the Mercedes pair of Lewis Hamilton and George Russell sixth and seventh.
Lance Stroll was ninth for Aston Martin and Yuki Tsunoda took the final point for Red Bull's Faenza-based RB team in their home race.
Verstappen held off Norris at a start without incident, the top four then running in grid order at a track where overtaking can be tricky.
What had looked like being one of the dullest races so far this year came to life as Norris began eating into Verstappen's lead in the closing laps.
He was 1.1 seconds adrift starting the final lap but just ran out of time.
"It hurts me to say but one or two more laps I think I would have had him," said the Briton.
"We are at a point now where we can say we are in the position with Ferrari and Red Bull. We have to get used to it. We are fighting for first and second now."
Red Bull team boss Christian Horner agreed: "Massive pressure. A great, great job by Max to withstand that pressure," he said.
"It was a race of two halves for us. The first half was very strong, but the second half of that last stint, Lando started to catch us very quickly.
"The cars are converging after the latest upgrades, they are looking very similar. McLaren were very quick at this circuit and Ferrari as well."
Williams' Alex Albon collected a 10-second stop and go penalty for a botched tyre change, with the Thai having to return to the pits for a second stop due to a suspected loose front wheel.
Aston Martin's Fernando Alonso also attracted attention when his front left brakes caught fire in the pits.
