CLEVELAND — Once upon an October, Josh Beckett got his first win at Progressive Field.

Four years later, with not nearly as much at stake, he got No. 2.

Beckett picked up first regular-season win in Cleveland, where he pitched an October gem to save Boston’s season in 2007, to lead the Red Sox to a 4-2 victory Tuesday night over the Indians, who couldn’t quite muster another late-inning rally.

Beckett (4-1) allowed one run and five hits in 62/3 innings and lowered his ERA to an AL-low 1.69.

Afterward, he was asked if it felt good to finally end his winless drought in Cleveland.

“I think I won here in the playoffs,” he said, straight-faced. “It’s not my first win at Progressive Field. Those wins (in October) are bigger anyway, aren’t they?”

With the Red Sox trailing 3-1 in the series and on the brink of elimination, Beckett won Game 5 of the 2007 ALCS, striking out 11 in eight dominant innings to beat CC Sabathia. Boston rallied to win the next two at home and made the World Series.

Jason Varitek hit a two-run homer in the seventh Tuesday night off Fausto Carmona (3-5), and Jonathan Papelbon got his ninth save as the Red Sox continued to make up ground in the standings. They are a league-best 15-7 in May and in the thick of the AL East race after an 0-6 start.

Adrian Gonzalez hit an RBI single for the Red Sox, who ended a five-game losing streak in Cleveland and have won 9 of 11.

Travis Buck homered in the ninth for the Indians, who had their four-game winning streak stopped and were hurt by running into outs four times.

Cleveland, which dropped to 19-5 at home, had a runner thrown out at third to end the second; Varitek gunned down would-be base stealers at second in the third and fourth; and Matt LaPorta got doubled up off first for the final out in the fifth.

“We didn’t do a very good job of taking care of our own 27 outs,” Indians Manager Manny Acta said. “When you’re facing a guy like Beckett, you have to make sure he works for every single one of those outs. We gave away a few on the bases.”

Beckett’s only loss this season came in Cleveland on April 5. Since then, he is 4-0 with five no-decisions in nine starts.

He beat the Indians without having much of a breaking ball.

“Josh should feel good about himself that he won in this fashion,” Varitek said. “It comes down to quality location with his fastball. We threw a lot more change-ups and cutters because he didn’t have his curve. He threw some real good sinkers.”

NOTES: John Lackey completed a bullpen session without trouble and remains on schedule to rejoin the Red Sox rotation in less than two weeks. “I felt pretty good,” Lackey said. “It’s a step in the right direction. I was able to let it go a little bit. I wasn’t feeling the same kind of bite in the elbow I felt before.”… The Red Sox outrighted lefty reliever Hideki Okajima to Triple-A Pawtucket. He was designated for assignment last week after Boston acquired left-hander Franklin Morales from Colorado.