Weaver (4-0) faced only two batters over the minimum. Chris Parmelee reached on a third strike passed ball with two away in the second and Josh Willingham drew a two-out walk on a 3-2 pitch in the seventh.
The other no-hitter in the majors this year was the perfect game thrown by Philip Humber of the Chicago White Sox against Seattle on April 21. Humber then gave up nine runs in his next outing.
Weaver struck out nine while throwing 121 pitches. It was the 10th no-hitter in franchise history and the fifth shutout of Weaver's seven-year career.
The Angels, who have been a major disappointment early in the season, won their third in a row.
Los Angeles backed up Weaver with a 15-hit attack, four of them coming from Howard Kendrick.
Kendrick hit a three-run homer in the fourth to complete the scoring and Kendrys Morales had a solo shot as part of a three-run third.
The loss went to Liam Hendricks (0-2), who gave up six runs on nine hits over 2 1/3.