BALTIMORE -- The Boston Red Sox are surging toward the postseason.

And in the process, they are dampening the chances of other contenders.

David Ortiz belted his 36th home run, a three-run shot in the seventh inning, and the Red Sox extended their winning streak to six games with a 5-2 victory over the Baltimore Orioles on Tuesday night.

Boston increased its lead over Baltimore to five games in the American League East. The Orioles have lost three out of four, but still hold a narrow margin for one of the two wild-card spots.

"I think there is growing confidence in our clubhouse daily," Red Sox manager John Farrell said. "We've responded to a number of challenges, whether it's on the road or coming from behind to win ball games 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."

Eduardo Rodriguez (3-7) picked up his first win since July 16 -- a span of 11 starts -- at the expense of his former team. He was charged with two runs on four hits with seven strikeouts over 6 1/3 innings.

Mookie Betts continued to pound Orioles' pitching and went 3-for-5 with two runs, while Jackie Bradley Jr. got his 26th homer.

"This was really huge," Bradley said. "We faced a really good team in Baltimore. 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."

The Orioles' Trey Mancini, who was the team's minor league player of the year in 2015, homered as the designated hitter in his major league debut. Mancini became the third player in franchise to accomplish that feat, joining Larry Haney (1966) and current second baseman Jonathan Schoop (2013).

Ortiz gave the Red Sox a 5-1 lead with a towering home run that ended Kevin Gausman's night. Gausman (8-11), who had won his past five starts, allowed five runs on 10 hits with five strikeouts over 6 1/3 innings.

The 36 homers by Ortiz are the most by any player in his final season, one ahead of Dave Kingman in 1986. Ortiz has six home runs in his past nine games at Camden Yards.

"I'll try to hit a couple more so nobody can reach me," Ortiz said. "It's just a number, man. I'm just trying to help this ballclub. I don't care about personal numbers. I care about winning."

J.J. Hardy cut the lead to 5-2 with a two-out infield single in the seventh off Matt Barnes. That was as close as the Orioles would get against Red Sox relievers Brad Ziegler, Koji Uehara and Craig Kimbrel, who picked up his 28th save.

Boston has won 11 of 14 and leads the season series with the Orioles 9-8 with two games remaining.

"We know how many opportunities there are and there's still an opportunity for us," Orioles manager Buck Showalter said. "They are a good team, like all the teams are at this level, but especially a team having as good of a year as they are. It's one thing to want to do it, as much as our guys want to, but you get a couple pitching performances against us like we've had the last two nights it's a challenge."

Gausman worked out of jams in the first and second innings to keep the game scoreless. The Red Sox broke through in the third on singles by Betts and Ortiz that put runners on first and third. Hanley Ramirez then provided a 1-0 lead on a fielder's choice.

While the Orioles' bats were silent, Bradley provided a 2-0 lead an inning later lead when he drilled a one-out homer to straightaway center.

"I was just leaving a couple of pitches too good early on," Gausman said. "A team like this, tough to repeat what I did in Boston, tried to keep us in the game as much as I could."

Rodriguez retired 11 consecutive batters before allowing a two-out walk to Manny Machado in the fourth. Mancini delivered the homer in his second at-bat, pulling the Orioles to within 2-1 in the fifth.

NOTES: Orioles LHP Wade Miley is feeling better after leaving in the fourth inning Sunday with a strained back muscle, Showalter. Miley could pitch over the weekend series against Arizona if there are no setbacks. Miley will go on paternity leave following Sunday's game. ... Red Sox 2B Dustin Pedroia was out of the lineup Tuesday to get treatment on his sore left knee. Farrell said Pedroia twisted the knee in a series against Toronto earlier this month. "I would be hopeful that he will be back on the field (Wednesday)," Farrell said. ... Baltimore OF Joey Rickard, who is on the 60-day DL with a right thumb ligament injury, has not been cleared to continue training at the team's minor league facility in Sarasota, Fla. Rickard has experienced some discomfort in his right hand.