PHOENIX, Ariz. — Mike Lowell began the game on the bench, but the Boston Red Sox third baseman is a student of the game.

He watches it intently, even when he’s not in the starting lineup. And as he watched Saturday night’s game against the Arizona Diamondbacks, Lowell was looking ahead, trying to figure out when manager Terry Francona might be calling on him.

So around the fifth inning, Lowell went back into the clubhouse, working with the trainers to find a taping job on his sprained left thumb that would enable him to hit. They tried it one way, he’d take some swings, and then they’d have to make some adjustments.

As the innings went by and the Red Sox crept back into the game, Lowell also did some work with hitting coach Dave Magadan, hitting off a tee, doing some soft-toss work and taking some light batting practice with Magadan throwing to him.

Francona’s SOS for Lowell came in the 10th inning, with the score tied, the bases loaded and one out.

And Lowell came through, delivering a fly ball to right field off Juan Cruz that was deep enough to permit David Ortiz to tag up and score the deciding run as Boston overtook the Diamondbacks, 4-3, before a record-setting crowd of 49,826 at Chase Field.

“He didn’t just sit around,” said Francona. “He started to get loose at one point and did some hitting. He handles his responsibility, whatever it is, the best he can all the time. That’s how professional he is.”

The victory was the third in a row for Boston, which began this road trip by losing the first three games. Julian Tavarez turned in a solid six-inning effort, but the Sox needed a two-run homer by Jason Varitek in the sixth and Varitek’s tying double in the eighth to lead to the win, which was claimed by Hideki Okajima (two scoreless innings) and saved by Jonathan Papelbon (14th).

Lowell’s winning RBI came in a role he doesn’t experience very often.

“Pinch hitting is a totally different mindset,” said Lowell, who battled back from an 0-an-2 count to 2-and-2 before lofting his game-winning fly ball.

Normally that pinch-hitting mindset is an aggressive one. See the first pitch you like and take a hack at it. The first pitch from Cruz was a fastball.

“That probably was the best pitch of the at-bat to hit,” said Lowell. “But it was coming so fast, it was a little too hard for my approach [into the ball].”

Lowell took the pitch for a strike, and then was frozen by a breaking ball for strike two and that 0-and-2 hole.

Still, he said he didn’t try to change anything in his approach.

“At 0-and-2 you’re still look to get a pitch you can do something with,” said Lowell. “You may expand your strike zone a bit. But I don’t adjust my swing in those situations. You work and work on your swing, and then to change it for one at-bat can be tough.

“I was just lucky I have more of a fly-ball swing than a ground-ball swing right now. And then I was praying that David’s choppy steps would get him home in time,” he joked.

Ortiz, who had opened the inning with a walk and moved up on singles by Kevin Youkilis and J.D. Drew (3-for-5), took off from third base a split-second after Carlos Quentin made the catch.

Quentin’s throw was way off to the first-base side of the plate, so Ortiz, whose legs took a beating playing first base the first two games of the series because there is no designated hitter in games in National League cities, scored easily.

“This playing first bull is killing me,” sighed Ortiz after the game, heading to the trainers room.

Ortiz got the bottom of the 10th off, as he was pulled with the Sox ahead and Francona looking to tighten his defense with Papelbon on the mound. So Lowell, sore thumb and all, stayed in the game at third and Youkilis moved from third to first.

And despite a couple of Diamondback baserunners against Papelbon, Lowell’s sacrifice fly stood up as the game-winner.

skrasner@projo.com