It wasn’t Alex Rodriguez’s best game by a long shot, but he still managed a three-run homer and a stupendous defensive play. That must be why he’s a perennial All-Star.

The third baseman committed a critical two-base throwing error in the second inning yesterday afternoon, leading to the first of the Tigers’ runs in a 10-8 win over the Yankees.

A-Rod entered the day in a 4-for-28 hitting funk before going 2-for-5 with a clutch seventh-inning homer, but his inability to make plays defensively clearly ate at him.

“We were happy about coming back,” he said. “We battled back, we thought we had a chance to win that game.

“They swung the bats very well today. We didn’t help defensively . . . I didn’t help them.”

Carlos Guillen led off the second with a slow roller A-Rod threw away for his seventh error of the year. He referred to the throw as a “dead fish;” it bounced past first baseman Jason Giambi and into the stands to allow Guillen to reach second.

Three batters later, A-Rod was unable to barehand Craig Monroe’s single, and the Tigers led 3-0 by the time the damage was done.

When A-Rod flied out to the track in center to end the third, he dropped his helmet onto the dirt between first and second base in a rare show of emotion.

The normally reserved, image-conscious superstar then chucked his batting gloves into the overturned helmet.

“I thought it was a tough day,” he said. “I thought it was just real heavy air.

“I crushed it. I thought that ball should’ve been gone.”

In the sixth, he made a tremendous play after backhanding a grounder on the third-base line. Rodriguez knew he couldn’t get speedy Alex Sanchez at first, so he spun in the air and threw to second to force out Eric Munson by a split-second.

The Yankees scored five times in the seventh to escape from a 10-3 hole, and A-Rod’s opposite-field, three-run homer off Franklyn German was the final volley.

Rodriguez’s 21st homer of the year carried over the right-field fence, surprising him.

“I hit it 50 percent less of how great I hit the other one,” he said. “When I hit that one, I said, That should be a fly ball to the first baseman.

“But I guess it was better placement. One of those days. Weird.”

With two outs in the ninth, he managed an infield single to bring the tying run to the plate. Giambi grounded out to second to end the game.

“I’m not putting pressure on myself at all,” Rodriguez said. “People talk about I’m not swinging the bat well.

“I think I’m swinging the bat great. And the difference in being red-hot on fire is just a couple feet here and there.”