Ortiz broke open a tight game with a three-run homer in the seventh inning, and Boston beat the Baltimore Orioles 5-2 Tuesday night for its sixth straight victory.
Jackie Bradley Jr. also homered for the Red Sox, who stretched their lead over third-place Baltimore to five games with 11 remaining. Toronto is in second place, four games back after a 10-2 victory at Seattle.
After sweeping four games from the Yankees, Boston has won the first two of this pivotal four-game series.
"This was really huge," Bradley said. "To get two wins right away is very vital for us. I think it will help us keep building on our momentum and finish strong."
Trey Mancini homered in his major league debut for the Orioles, who are 1 1/2 games ahead of Detroit for the second AL wild card.
The Red Sox are 11-3 in their last 14 games and a major league-best 13-5 in September.
"I think there is growing confidence in our clubhouse daily," manager John Farrell said. "We've responded to a number of challenges, whether it's on the road or coming from behind to win ballgames in the division. Those are key. When you succeed in those, that's a snowball effect that takes place.
"To balance that out, no one is taking any of that for granted."
"I still can't figure out how he can swing so hard on balls up and in and then cover a pitch down and away, but that's why he's the hitter he is," Orioles catcher Matt Wieters said.
Ortiz guessed correctly that Gausman would throw a fastball.
"I had to shoot for something. Experience played out in that at-bat," the slugger said. "I told myself, `I've got to either shoot for a fastball or a splitter.' But I know he's throwing his best fastball right now. So I'm going to go for a fastball. And then he threw the fastball."
Playing in his final season, Ortiz has 36 home runs and 121 RBI. Big Papi has hit eight home runs against the Orioles this season -- including two in this series -- and 54 for his career.
Betts also extended his run of success against Baltimore, going 3 for 5 and scoring twice. He is 16 for 31 at Camden Yards and has scored 16 runs in eight games.
Eduardo Rodriguez (3-7) allowed two runs and four hits in 6 1/3 innings for Boston, his first win in 11 starts since July 16.
Craig Kimbrel worked the ninth for his 28th save.
After giving up four hits in eight scoreless innings last week at Boston, Gausman yielded five runs and 10 hits in 6 1/3 innings.
Boston went up 1-0 in the third when Betts singled and scored on a grounder by Hanley Ramirez. Bradley hit his 26th homer in the fourth.
Rodriguez retired his first 11 batters and held Baltimore without a hit until Mancini connected with two outs in the fifth. The rookie sprinted around the bases, taking about half the time Ortiz did during his home run trot in the seventh.
The Orioles were quick to turn the page after the defeat, but Mancini will never forget this night. He became the third Orioles player to homer in his first game, following Larry Haney in 1966 and Jonathan Schoop in 2013.
"It was a really special moment, something that I've definitely been waiting for my whole life," the rookie said.
Red Sox: Farrell gave 2B Dustin Pedroia (knee) the night off but expected him back in the lineup Wednesday.
Orioles: LHP Wade Miley is expected to leave the team after Sunday's game against Arizona to join his wife, who is expecting. Manager Buck Showalter said the pitcher might miss the Toronto series that begins Tuesday.
Red Sox: Clay Buchholz (7-10, 5.20 ERA) looks to extend a three-game winning streak Wednesday night. He is 0-2 with a 6.35 ERA against Baltimore this season.
Orioles: Unbeaten in four starts since Aug. 25, Ubaldo Jimenez (7-11, 5.94) is 2-5 with a 7.39 ERA lifetime against the Red Sox.
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