Bundy (1-0) allowed one run, three hits, no walks and hit one batter in 6 2/3 innings as part of an impressive first start after being acquired from Baltimore in a trade last December.
''I don't really try to put any extra pressure on or anything,'' Bundy said. ''I just try to go out and compete like I've always done. I love to compete in the game of baseball.''
The performance helped the Angels bounce back from an extra-inning loss in the opener. Upton hit a solo homer off Sean Manaea, and Andrelton Simmons and David Fletcher also had run-scoring hits for Los Angeles.
Bundy had seven strikeouts and needed only 90 pitches in an efficient performance. He was replaced after allowing a two-out double to Stephen Piscotty in the seventh.
Robbie Grossman hit an RBI single off Keynan Middleton to get the A's on the board.
Hansel Robles pitched the ninth for his first save after taking the loss in the opener.
Manaea looked sharp early, retiring the first 11 batters on just 32 pitches. Then he ran into trouble and couldn't even make it out of the fifth inning.
''He was great. I mean, what did he have, 39 or 40 pitches going into the fifth?'' manager Bob Melvin said. ''It just happened pretty quickly with three batters that he got some balls in the middle of the plate, which he hadn't been doing, and the next thing you know we had to get him out. But I was really encouraged by the way he threw compared to maybe what we saw in the Bay Bridge series.''
Upton broke through with a solo homer with two outs in the fourth to get the Angels on the board. Manaea then allowed three straight hits with two outs in the fifth. Simmons hit an RBI double and Fletcher added a two-run double that knocked out Manaea and made it 4-0.
''We just kept after him,'' Angels manager Joe Maddon said. ''It wasn't like we were having awful at-bats. He was just on top of his game and strike throwing was real accurate for him. Upton's homer dented him a little bit.''
The A's failed in their attempt to start a season 2-0 for the first time since 2004.
Angels: New 3B Anthony Rendon took some grounders and swings before the game as he works his way back from an oblique injury.
Athletics: The A's are mostly healthy outside of starter A.J. Puk, who is out for at least two weeks with a shoulder injury.
Hard-throwing A's reliever Jesus Luzardo had an impressive season debut in relief. He struck out two in three scoreless innings. Luzardo was sharp as a late-season call-up last year with two saves and a 1.50 ERA in six relief appearances and is being counted on in a bigger role this season.
Angels two-way star Shohei Ohtani is set to make his first appearance on the mound since Sept. 2, 2018, after not pitching last season following elbow surgery. Ohtani is expected to be the Sunday starter for the Angels this season and is under no pitch limit. Mike Fiers will start for the A's in his first appearance since revealing to The Athletic in November that his former team, the Houston Astros, had stolen signs using a camera in center field during their run to the 2017 World Series championship.
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