NEW YORK -- If the Boston Red Sox can't be a part of the pennant race, at least they can impact the playoff push in both leagues.

Center fielder Mookie Betts homered and scored two runs Saturday and right-hander Joe Kelly threw 7 1/3 innings of one-run ball to win his sixth straight start as the Red Sox beat the New York Mets 3-1 at Citi Field.

The Red Sox (60-69) are seven games behind the Texas Rangers in the race for the second American League wild card, but have won the first two games of the three-game series to improve to 10-5 under interim manager Torey Lovullo, who took the reins after John Farrell was diagnosed with lymphoma.

"It's fun to watch (and) come to the ballpark," Kelly said. "We're not in it right now. Watching the way everyone's playing, it's pretty fun."

Boston's last 12 games have been against teams either in playoff position or within six games of a wild-card spot entering Saturday.

"I think we're all in a really good place and I'm really proud of these guys," Lovullo said. "Our youngsters come in here and they're growing up before our very eyes."

Kelly continued his maturation Saturday, when he survived a 30-pitch first inning to last 7 1/3 innings for the second time this week and just the third time in 70 career starts. The 27-year-old carried a shutout into the seventh and allowed the one run on five hits and two walks while striking out two.

"Joe Kelly set the tone for us," Lovullo said. "Six straight wins -- I can't say enough about what he did to give us a chance to win today."

Kelly has a 2.68 ERA in his last six starts and is 6-1 with a 3.74 ERA in eight starts since being promoted from Triple-A Pawtucket on July 22. He was 2-5 with a 5.65 ERA prior to his demotion on June 25.

Kelly said the key to his success has been mixing in off-speed pitches to compliment his fastball, which regularly reached 96 mph. On Saturday, Kelly said he relied largely on his change-up to keep the Mets off-balance.

"It's been a big point of emphasis that no matter what team we're facing, I have to throw off-speed," Kelly said. "Throwing all fastballs, obviously that hasn't worked out."

The Red Sox defense got plenty of work Saturday behind Kelly, who induced 12 ground balls, including double plays in the third and fifth.

"It's fun to watch when you know you can let the guys put the ball in play," Kelly said.

Kelly and Mets right-hander Jacob deGrom were locked in a scoreless duel until the sixth, when Betts delivered a leadoff single, took second on a wild pitch and scored on a double by third baseman Pablo Sandoval.

Sandoval went to third on a fly out by shortstop Xander Bogaerts. After walking first baseman Travis Shaw, deGrom got Holt to ground to first. Sandoval took off for home but Daniel Murphy attempted to get the double play instead of throwing to the plate and Holt beat out the relay throw.

"Joe Kelly today came up, kept them with a zero the whole time until we were finally able to scratch across the runs," Betts said. "You've got to put up some runs after that kind of performance."

Betts provided an insurance run with a two-out solo homer in the seventh.

The Mets scored in the bottom of the seventh, when second baseman Kelly Johnson singled and came home on a double by third baseman Juan Uribe. But Kelly, left-hander Tommy Layne and right-hander Jean Machi combined to hold the Mets without a hit over the final two innings.

Machi tossed a perfect ninth for his third save.

"We know that everybody's going to contribute in the game, some way and somehow," Betts said. "We're enjoying it now."

Uribe and right fielder Curtis Granderson had two hits apiece for the Mets (71-58), whose lead over the Washington Nationals in the National League East fell to six games, pending the Nationals' game later Saturday against the Miami Marlins.

The Mets have scored just five runs in their last two games after scoring 73 runs in a seven-game winning streak that ended Friday.

"We've been smashing the ball and today, the last two games, we have not," Mets manager Terry Collins said. "Today we looked a little tired."

DeGrom (12-7) allowed two runs on four hits and two walks while striking out 10 over six innings. He retired the first nine batters he faced and didn't allow a hit until Holt's leadoff single in the fifth.

NOTES: Red Sox C Ryan Hanigan (tight right calf) was scratched about an hour before the first pitch and replaced in the lineup by C Blake Swihart. ... Red Sox LF Hanley Ramirez (right shoulder), who was a late scratch Friday, didn't start and was unavailable off the bench. Interim manager Torey Lovullo also said he wouldn't use RHP Junichi Tazawa, who tweaked his right hip and groin while turning a double play in the 10th inning Friday. ... Mets 3B David Wright received a scheduled day off. He has played in four of six games since being activated Monday from the disabled list after missing 115 games with a hamstring injury and spinal stenosis. ... With the Mets' bullpen taxed after two straight extra-inning games, RHP Bartolo Colon tossed a scoreless ninth inning. It was Colon's first relief appearance since April 14, 2011.