The Red Bull driver, starting from pole position at Austin's Circuit of the Americas with Norris alongside, finished 0.395 seconds clear of Mercedes' George Russell, with Carlos Sainz third for Williams and Lewis Hamilton fourth for Ferrari.
The eight points for victory left four-time world champion Verstappen 55 adrift of championship leader Piastri with the main grand prix to come on Sunday and five further rounds after that, including two more sprints.
"The start was good, then of course there was the safety car because of the turn one incident," said Verstappen after just the sort of perfect outcome he needs to have a chance of a fifth successive title.
"Then it took a few laps after the safety car to have a decent pace.
"I do think we need to be a bit better in race trim to be able to fight the McLarens because we haven't seen anything of them."
Norris and Piastri's race was over in a matter of metres, the Australian's car hit by Sauber's Nico Hulkenberg at the first corner and pitched onto his teammate's.
The safety car was deployed, with debris strewn across the track.
"Someone just wiped me out, I'm out," said Norris, a blameless victim who tried to continue but stopped on track.
Piastri, 22 points clear of his teammate at the top of the standings, made it back to the pit lane but retired with a broken suspension.
"I had a pretty good start, we both went pretty deep into Turn 1 and I tried to cut back, and got a hit, so obviously not a great way to start the day," said the Australian.
"That was terrible. Neither of our drivers is to blame there," McLaren boss Zak Brown told Sky Sports television.
Jenson Button, the 2009 world champion, was less sure: "From a racing driver's point of view, it was more on Oscar. Lando's not even in this conversation. He was just unlucky to be there," he said.
Ferrari's Charles Leclerc was fifth after being overtaken by Hamilton, Alex Albon finished sixth for Williams, with Verstappen's teammate Yuki Tsunoda seventh and the final point going to Mercedes' Kimi Antonelli.
Haas's Oliver Bearman finished eighth on track but collected a 10-second penalty for going off and gaining an advantage.
Russell and Verstappen both ran wide as the Briton tried to pass at the midpoint of the race, but the leader retained the position.
"I knew that was the only chance. I had to try it," Russell said over the radio after being complimented by team boss Toto Wolff on a "good send".
The 19-lap race finished behind the safety car after Aston Martin's Lance Stroll, whose teammate Fernando Alonso was caught up in the first-lap mayhem, and Haas's Esteban Ocon collided three laps from the end.