Dinelson Lamet was brilliant in taking a no-hitter into the seventh inning and Tatis continued his remarkable power surge with a two-run homer off Bumgarner, who allowed four of San Diego's club-record six long balls as the Padres beat the Diamondbacks 9-5 on Sunday.
Machado homered twice off Bumgarner. Wil Myers, Francisco Mejia and Ty France also went deep for San Diego.
Lamet (2-0) had allowed only one baserunner, on a hit by pitch, until Kole Calhoun homered on a 2-0 pitch leading off the seventh. Lamet got two more outs before manager Jayce Tingler pulled him in favor of rookie Luis Patino.
Lamet retired the first 14 Diamondbacks batters, struck out 11 overall and walked none in 6 2/3 innings. The hard-throwing right-hander hit Andy Young with a pitch with two outs in the fifth but otherwise kept Arizona off the bases until Calhoun's homer.
The Padres remain the only major league team without a no-hitter, having played 8,154 games since 1969 without one.
''The saying we have is, hope is the last thing you lose,'' Lamet said. ''I'm not out there first pitch, first hitter, thinking, `OK, today I'm going to throw a no-hitter.' I'm going out there to get outs. I get ahead of a guy, get two strikes, I'm trying to get quick outs, I'm trying to get you out with as few pitches as possible. I'm attacking. So in my mind, the result is going to take care of itself.''
Machado said Lamet had been locked in since Saturday.
''He told me yesterday, `Hey, hold down the fort today because tomorrow I'm coming in with some gas and I'm going to put out that fire.' ... Today since the first pitch, he was ready to go,'' Machado said.
Lamet confirmed that conversation, saying: ''Luckily, we were able to go out there and I was able to give a good effort and we won the game.''
San Diego took two of three in the series and is 5-2 against Arizona this season. With the Padres leading 9-1, Diamondbacks catcher Carson Kelly pitched the eighth. He allowed rookie Jake Cronenworth's leadoff double before retiring the side.
Arizona hit a pair of two-run homers off San Diego's bullpen in the ninth.
Machado homered off Bumgarner in the first and second, and Myers also connected against the struggling left-hander, who was finished after two innings, matching his career low.
France and Mejia homered off reliever Taylor Widener in the third.
The six homers were the most the Padres have ever hit at home. It was the first time they've hit six homers in the first three innings, and just the fifth time that's happened in the majors in 20 years.
Tatis, the son of the former big league infielder, drove a 2-2 curve an estimated 418 feet into the second deck with two outs in the second, his eighth homer, for a 5-0 lead. The 21-year-old shortstop has hit five in the last four games and six in six games. He hit four in this series, including leadoff shots Friday and Saturday nights. He connected twice Saturday night.
Tatis has been on base in 17 straight games dating to his last game of 2019, on Aug. 13. He missed the rest of the season with a stress reaction in his lower back but still finished third in NL Rookie of the Year voting.
''Being 21 years old, he's a freak athlete, he's getting stronger, he's lifting, he's running, he's moving well,'' Tingler said. ''He's able to get barrel to ball, maybe on some more pitches he hadn't been able to. He's been working on his swing, shortening that up. You see the way the ball's coming off the bat. He can leave the ballpark.''
Machado homered with one out in the first and Myers hit a two-run shot with two outs. Myers' fifth homer brought in France, aboard on a walk.
After Tatis' homer, Machado connected again, his third.
France greeted Widener with a homer leading off the third, and Mejia hit a two-run drive off the right-field foul pole with two outs. They were the first of the season for both.
Bumgarner (0-3) continues to struggle with the Diamondbacks, who gave him an $85 million, five-year contract in December after he spent a decade with the San Francisco Giants, helping them win three World Series titles in five seasons.
He allowed six runs and five hits in two innings, struck out two and walked two.
Arizona manager Torey Lovullo said the 31-year-old Bumgarner exited after experiencing back spasms.
Bumgarner also lost to the Padres on opening day, 7-2.
Young hit his first career homer, a two-run shot off Patino with one out in the ninth, and Nick Ahmed had a two-run shot off Tim Hill.
Diamondbacks: LHP Robbie Ray (1-2, 9.45 ERA) is scheduled to start the opener of a three-game series at Colorado. He needs nine strikeouts for 1,000. The Rockies are set to counter with RHP Jon Gray (0-1, 3.31).
Padres: RHP Garrett Richards (0-1, 4.60 ERA) starts the opener of a four-game series at Dodger Stadium on Monday night. The Dodgers counter with RHP Dustin May (1-0, 2.63).
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