The three rookies at the bottom of the lineup proved him wrong.
"I thought we might have to score runs in a little bit different fashion, especially at the bottom of the order," Girardi said. "Those guys kept hitting triples."
Making his second straight start in place of Jeter (right oblique), rookie Ramiro Pena tripled and scored from the eighth spot. Right behind him, rookie catcher Francisco Cervelli picked up his first career RBI as the Yankees finished with 11 hits, including eight for extra bases, and improved to 11-0 when holding their opponent to three runs or less.
"It gives us a little boost," Gardner said of the big night by the bottom third. "We've got a lot of interchangeable parts here."
Batting in the seventh spot, Gardner hooked a 1-1 breaking ball over the wall in the right-field corner in the second before hitting a triple and scoring in the fifth.
"At the time, I didn't know that was his first one," Yankees slugger Mark Teixeira said of Gardner's homer. "I just gave him a handshake and then everyone started saying it was his first one and I got real excited for him. There's not many better feelings than your first home run."
Gardner's teammates presented him with a dummy memento ball, spelling his name wrong, writing the wrong date and saying the homer was a solo shot, not a two-run drive. He said the real one will go into his trophy case alongside his first career hit.
Teixeira finished 2-for-4 with a double and two RBIs, raising his average to .202.
"One of the best things about tonight was Tex," Girardi said. "That's the Tex we're used to seeing most of the time. He's not going to do it every night but that's the type of hitter he is."
Every Yankees starter except right fielder Nick Swisher reached base safely at least once. Besides Swisher, the only Yankees starter not to get a hit was Alex Rodriguez, who went 0-for-2 with three walks.
Jeter has not played since Sunday because of a sore right oblique and Girardi said he might not play again until Friday. Matsui left Tuesday's game after one at-bat with a tight right hamstring and is day-to-day.
Johnny Damon started as the DH and led off Wednesday while Swisher batted second.
Pettitte (3-1) allowed two runs and five hits in six innings to win for the first time since April 21.
"They made it hard on me," Pettitte said. "By the sixth inning I was running on fumes a little bit."
Melky Cabrera led off with a double and scored when Gardner connected. Pena tripled and scored one out later on a triple by Damon. Swisher grounded out but Teixeira hit an RBI double, Rodriguez walked and Cano knocked Richmond out of the game with a run-scoring single.
The AL rookie of the month for April, Richmond (4-2) has lost both his starts in May. He allowed five runs and seven hits in 1 2/3 innings, the shortest outing of his 12-start career.
"Plain and simple, fastball control needs to be better," Richmond said. "Obviously you want to get the fastball across better and you can work off your other pitches from there but if your fastball isn't getting across down in the zone, it's going to be a rough outing."
John McDonald replaced Hill in the field in the fifth. Hill fouled a ball off his left shin in the third but he said after the game it wasn't serious.
Damon has 12 extra-base hits in his past nine games. ... Right-hander Brian Bruney (shoulder) threw a 25-pitch bullpen session before the game and will throw another on Friday when the Yankees return home. ... Catcher Jorge Posada (right hamstring) took batting practice, threw and ran in the outfield at the Yankees' spring facility in Florida. He might be ready to play in a minor league game by early next week. Also in Tampa, right-hander Sergio Mitre (elbow) allowed one run and three hits and struck out eight over four innings in his third extended spring training game. ... Toronto left-hander Ricky Romero (right oblique) made his second rehab start, pitching 5 1/3 innings at Double-A New Hampshire. He allowed two runs, one earned, and three hits, walked five and struck out four.