Weaver struck out nine and walked one. The Twins never came close to getting a hit against the All-Star right-hander.
"It was an easy ride," Weaver said.
Phil Humber of the Chicago White Sox threw a perfect game at Seattle on April 21.
Weaver (4-0), a California native who played at Long Beach State, began the ninth by quickly retiring Jamey Carroll on a routine fly and striking out Denard Span looking.
Weaver then got Alexi Casilla to lift a long fly that right fielder Torii Hunter easily caught at the warning track. The Angels' ace watched his Gold Glove outfielder make the play, and put his hands on his head as the Angels rushed out to mob him.
"Spiderman out there. I knew he had a bead on it," Weaver said of Hunter. "Casilla put a charge in it and Spiderman tracked it down."
An inning earlier, Weaver and his teammates could only hope when Trevor Plouffe lined a shot that hooked foul a few feet before reaching the left-field foul pole.
After that, Weaver finished off the Twins in fast order.
His gem complete, Weaver hugged his wife, his dad and his mom, who was crying on the field.
"I was locked in for the most part," he said. "My mom, dad, wife, this was awesome."
Weaver will soon get a chance to do it again against the Twins — his next start is scheduled for Monday at Minnesota.
"I'm at a loss for words right now. It hasn't kicked in yet," he said. "Thank you for all your support. Couldn't have done it without the defense. The guys were picking me up left and right."
This was the second Angels no-hitter in less than a year — Ervin Santana pitched one July 27 at Cleveland — and the 10th for the Angels franchise, including four by Nolan Ryan.
Weaver threw 121 pitches, and the cheers from the crowd of 27,288 kept growing louder.
"Fastball command was good. Able to fill up the zone get some early strikes," Weaver said.
"This is so surreal I can't even believe this," he said.
Only one Minnesota batter reached base through the first seven innings, and that was when catcher Chris Iannetta committed a passed ball on strike three to Chris Parmelee with two out in the second. Josh Willingham drew the only walk Weaver allowed with two outs in the seventh.
"He dominated us, there's no question about it," Span said. "He was doing everything. He kept us off-balance, changed speeds and finished strong."
The no-hitter was the highlight for a 29-year-old pitcher who has already compiled quite a resume.
Weaver finished second in the AL Cy Young voting last year after going 18-8 with a 2.41 ERA. He and winner Justin Verlander were the only pitchers listed on every ballot.
Kendrys Morales and Howie Kendrick homered to back Weaver, not that he needed much support.
The Angels' three-game sweep of the Twins included a complete-game three-hit shutout on Tuesday night by Jerome Williams, who retired 18 of his last 19 batters.
The Twins haven't had a hit in the last 15 innings.
It was the first time the Angels had back-to-back complete game wins since 1993 when Chuck Finley and Mark Langston did it.
The Angels built a 6-0 lead against Australian-born Liam Hendriks (0-2).
NOTES: Kendrick hit his fourth homer of the season and drove in three runs.