NEW YORK -- Asked about trying to hit a home run for the cycle in the fourth inning, New York Yankees center fielder Brett Gardner said he was trying to use his "A swing."

Gardner had three of those swings and the rest of the Yankees had a lot more flawless cuts.

Gardner came within a home run of the cycle, designated hitter Alex Rodriguez hit a three-run homer and drove in five runs and switch-hitting right fielder Carlos Beltran homered from both sides of the plate in New York's 14-3 rout of the Detroit Tigers on Saturday night.

Gardner nearly became the first Yankee to get the cycle since Melky Cabrera in August 2009. He tripled in the first, doubled in the second and singled in the third against Detroit right-hander Alfredo Simon (7-4).

If Gardner wasn't going for the cycle, he likely would have come out of the game, but he stayed in and had three chances at the achievement.

Gardner's near-miss was the only thing that went wrong for the Yankees, who tied a season high with five home runs, had a season-high 18 hits and won for the 11th time in their last 12 home games.

"I was aware of it," Gardner said. "The game was a little out of hand. So I'm not necessarily going up there and taking my usual patient at-bats, trying to grind out at-bats like usual. I was just go up there looking for a good pitch to hit and if it happens, it happens. I was just trying to go up there and take my A-swing."

Yankees manager Joe Girardi said, "He's been really good. When he goes, a lot of times we score a lot of runs and he creates a lot of havoc on the bases. Just an outstanding job by him tonight and our whole offense just making Simon work tonight."

Gardner's near-cycle was not the biggest achievement during New York's latest home win.

Rodriguez hit his 668th career home run and also drove in runs in his first two-plate appearances after becoming on Friday night the 29th player to reach 3,000 hits.

"He (Gardner) had an unbelievable game," New York catcher Brian McCann said. "Both (Gardner and Rodriguez) are equal (achievements)."

Beltran wound up with his 37th career multi-homer game and homered from both sides of the plate for the 12th time. He connected from the left side off Simon in the third and homered from the right side off left-hander Ian Kroll in consecutive innings.

"Right now, we're getting results and that's important," Beltran said.

Besides the big nights from Gardner, Rodriguez and Beltran, the Yankees also had solo home runs from shortstop Didi Gregorius and left fielder Chris Young. They also had RBI singles from Young, McCann and third baseman Chase Headley.

Right-hander Nathan Eovaldi (6-2) pitched on three days' rest and allowed two runs and three hits in six-plus innings.

While the Yankees enjoyed their most productive game of the season, the Tigers (34-34) dropped their fourth straight, fell to .500 and held a brief team meeting afterward.

The game was so lopsided that Detroit manager Brad Ausmus pulled starting second baseman Ian Kinsler, first baseman Miguel Cabrera and left fielder Yoenis Cespedes after the fifth when the deficit was 13 runs.

"We just need to play better baseball," Detroit designated hitter Victor Martinez said. "They came out swinging. Everything was going (well) for them, nothing for us. A 2-1 loss, a 1-0 loss, 14-3, it's still a loss."

The Tigers used five pitchers and finished the game with reserve infielder Josh Wilson on the mound. That came after Simon allowed seven runs and eight hits while working deliberately through 2 1/3 innings in his second-shortest career start.

"If we keep playing like this, we're going nowhere," Martinez said. "There's no secret. We got to go out there and put a better effort, better at-bats and make better pitches. That's the only way we're going to win ballgames."

The Yankees took a 1-0 lead when Gardner scored on Rodriguez's fielder's choice. Gardner scored when third baseman Andrew Romine's throw to the plate deflected off his helmet for an error.

After a solo home run by Gregorius and a sacrifice fly by Rodriguez in the second, the Yankees scored five in the third on Beltran's first home run, a single by Headley that knocked out Simon and Rodriguez's 14th home run of the season.

Beltran's second home run made it 9-0 and Young's single gave the Yankees double digits runs. New York's 11th and 12th runs came in the fifth when McCann singled and Beltran was hit by a pitch.

The Yankees scored their final two runs on Gregorius' groundout and Young's home run off Wilson in the eighth.

Detroit's only runs came in the seventh on a double by right fielder J.D. Martinez, a wild pitch by Yankee reliever Bryan Mitchell and a single by McCann.

NOTES: Yankees rookie OF Mason Williams had an MRI on his jammed shoulder and did not play after injuring it in the fifth inning Friday. ... The Yankees held their 69th annual Old-Timers Day celebration and honored former 2B Willie Randolph (1976-1988) with a plaque in Monument Park. Randolph won six World Series with the Yankees as a player and coach (1977, 1978, 1996, 1998, 1999 and 2000). ... The Yankees also honored former RHP Mel Stottlemyre, who also was pitching coach, with a plaque in Monument Park. Stottlemyre is dealing with multiple myeloma, the same form of cancer he had in 2000 and 2011. ... Detroit DH Victor Martinez was in the lineup for the second straight day after being activated from the disabled list Friday. ... RHP Ivan Nova, coming back from Tommy John surgery, is expected to rejoin the Yankees next week.