BOSTON — There was no doubt in Red Sox right fielder Eric Hinske’s mind what he had to do.

Mike Rabelo’s long, hard-hit fly ball was bending toward the corner with a runner at second and two outs in the fifth inning and Detroit holding a one-run lead over Boston.

“I had to catch it, no matter what,” said Hinske,a converted infielder who already had had some outfield misadventures because of a tough wind at Fenway Park.

And he did make the catch, but it wasn’t your basic grab. Hardly.

It was a sensational, face-first, head-banging diving catch on the hard-packed dirt of the warning track in the right-field corner where the wall begins to jut out, Hinske’s head bouncing up and quickly back down again, leaving him prone and in pain.

But the ball stayed in his glove.

And that wasn’t the end of Hinske’s heroics.

Hinske, in the starting lineup because J.D. Drew (bruised back) was unable to play, clouted a tie-breaking two-out two-run homer into the Red Sox’ bullpen near the triangle end in the seventh, giving Boston a 4-2 victory over Detroit last night and a sweep of the day-night doubleheader.

The homer for Hinske, a left-handed hitter, was his first of the year, coming off left-hander Wilfredo Ledezma.

“It was a complete game for him,” said Sox third baseman Mike Lowell. “He saved a potential rally with his glove and won us a game with his bat.”

Hinske was the second unlikely star for the Sox yesterday. In the first game, yesterday afternoon, Julian Tavarez limited the Tigers to one run on four hits in seven innings as Boston edged Detroit, 2-1.

Hideki Okajima and Jonathan Papelbon (11th save) finished up for Tavarez, who was supported offensively by run-scoring singles from Manny Ramirez (first inning) and Kevin Youkilis (third).

The twin wins enabled the Red Sox to take three of four from the Tigers in a series matching two of the best teams in the American League. They also expanded Boston’s A.L. East lead to a whopping 9½ games over the New York Yankees.

While Tavarez deserved his time in the postgame spotlight, it was Hinske, a role player who has embraced his role as a utility player on a good team, who took star of the day honors.

Not that the night began on a promising note for Hinske.

Hinske’s highlight-reel catch came out of the blue. He had been having some serious issues with the wind in right field.

He was barely able to track down Sean Casey’s bases-loaded drive on the warning track in front of Detroit’s bullpen with two outs in the first. And he broke the wrong way on Rabelo’s fly ball, failing to catch with a dive as he raced in with one out in the second.

And along the way, Hinske was watching a couple of ground-rule doubles zip past him to his left and to his right.

“He got every kind of ball there is known to mankind,” said Lowell.

But in the fifth, Hinske came through for the Sox, robbing Rabelo with his all-out dive. The ball found its way into Hinske’s glove at just about the same time Hinske was crash-landing.

“I had to sell out on that one. I had to lay out for it,” said Hinske.

Hinske lay prone, face down in the dirt, for several seconds before rolling over. His teammates on the field, including pitcher Curt Schilling, the beneficiary of the catch, as well as manager Terry Francona and trainer Paul Lessard, ran out to check on Hinske.

“I heard Coco say, ‘Dude, you all right?’ Someone said, ‘He’s out’ and I heard ‘Sweet catch.’ I was fine. Schilling came all the way down there. That was cool. It was cool to hit your face and still catch it.”

Schilling, among others, was impressed by the play.

“Unbelievable,” said Schilling. “One of the best catches I have ever seen anywhere.”

Eventually Hinske got up and trotted off the field under his own power to a rousing ovation for his all-out effort.

“I got out there and he said, ‘I’m okay. I just hit my head,’ ” said Francona. “He just willed himself to make that catch.”

The ovation for Hinske got even louder when he crushed Ledezma’s 2-and-0 fastball to right-center for the game’s big homer.

“He had a tough day at the plate going into that at-bat,” said Francona. “He took a beautiful swing.”

“I was in a hitter’s count and I was looking for a good pitch to hit and I got it and out a good swing on it,” said Hinske.

And as a result of Hinske’s glove and bat, the Red Sox finished off a very good day at the ballpark, not to mention a very solid series against one of the best teams in the American League.