With Randy Johnson on short rest, Jason Giambi’s big day helped make his job easy.

Giambi hit one of four Yankees homers and doubled twice, and Johnson gave New York seven clutch innings in a 12-3 victory yesterday over the sinking Baltimore Orioles.

Alex Rodriguez also connected, while Giambi, Gary Sheffield, and Hideki Matsui all homered for the second consecutive game.

“Today was just one of those magical days where everyone was swinging the bat well,” Rodriguez said.

Derek Jeter and Ruben Sierra added three hits apiece for the Yankees, who swept the two-game series and have won four straight to move within a half-game of second-place Baltimore.

“We’re lucky,” manager Joe Torre said. “We understand if you’re hovering around the .500 mark in some other division, that doesn’t bode well for you.”

With their pitchers struggling, the Orioles have lost 11 of 13.

Starting on three days’ rest in the regular season for the first time in 10 years, Johnson (8-6) bounced back from an awful performance in Detroit last Friday, when he was roughed up for seven runs and nine hits in five innings.

But he threw only 80 pitches in that one, and was eager to get back on the mound.

Good thing for the injury-riddled Yankees, who used five pitchers in a 13-8 win Monday, including a spot start by reliever Tanyon Sturtze – so they needed a lengthy outing.

The Big Unit delivered, retiring his first 12 batters with five strikeouts before Miguel Tejada’s infield single. He threw 92 pitches and fanned eight without walking a batter for his 254th win.

“His pitch count early was terrific and I think that was a big reason he was able to last seven innings,” Torre said. “He looked a little relaxed and yet very focused.”

Johnson gave up seven hits, including a two-run homer by Chris Gomez – his first this year. The left-hander improved to 5-1 in regular-season starts on three days’ rest. His last was October 2, 1995, for Seattle against the Angels, when he pitched the Mariners to the AL West title.

“He was pretty sharp – with a 10-run lead,” Mazzilli said.

Also pitching on three days’ rest while the Orioles use a four-man rotation until the All-Star break, Rodrigo Lopez (7-5) was ineffective – and his defense was just as bad. He gave up a career-high 10 runs – five earned – and a season-high 11 hits in three-plus innings, dropping his third straight start.

Coming off his first multihomer game in two years, Giambi connected for his eighth of the season leading off the second inning. He got a standing ovation when he departed for a pinch-runner after his second double in the sixth.

“He’s been killed by everyone,” Rodriguez said. “To see him still fighting and persevering, he’s very easy to cheer for.”

Jeter opened the third with a single, and Gomez booted Robinson Cano’s potential double-play grounder to first, leaving runners at the corners. Jeter then got caught in a rundown on a bouncer to third, but third baseman Melvin Mora dropped a return throw from Fasano for his second error of the game, allowing Jeter to score.

Matsui hit an RBI single, Giambi had a run-scoring double, and Sierra grounded a two-run single through a drawn-in infield, making it 6-0.

Jeter started the fourth with his third single, Cano doubled, and Sheffield hit a three-run shot for his 430th homer, tying Jim Thome for 34th on the career list.

Rodriguez followed with his 21st home run this season for a 10-0 lead, chasing Lopez.

Matsui added a two-run drive off James Baldwin in the sixth.