BALTIMORE — Robbie Ross Jr. pitched an inning for the Texas Rangers on that May night in 2012 when Josh Hamilton hit four home runs at Camden Yards.

Ross never imagined he could be more impressed with a hitter. Then Mookie Betts came along.

Betts hit two more home runs, the second to win the game in the eighth inning, as the Red Sox beat the Baltimore Orioles, 5-3, on Tuesday night.

Betts drove in all five runs as the Sox won their fifth straight. He has five home runs and 13 RBIs in the last three games.

“Freakish,’’ Ross said. “That unbelievable. It’s unreal . . . I’ve never seen anything like this. It’s night and day. Just boom, boom, boom; he’s going to get it going. It’s pretty special. He’s clutch as you can get, man.’’

A day after they beat the Cleveland Indians, 3-2, the Sox beat another playoff-quality opponent on the road. These are the impossible-to-script moments that change the course of a season.

“Some momentum, definitely,’’ Jackie Bradley Jr. said. “Mookie has been able to be the spark for us. It’s been fun.’’

At 66-52, the Sox are now tied with the Orioles in the American League East standings, a game behind the Toronto Blue Jays. The brief series ends Wednesday with David Price facing Dylan Bundy.

There was a downside for the Red Sox: Starting pitcher Eduardo Rodriguez left the game two pitches into the fifth inning with a 3-0 lead and a no-hitter. He had a tight left hamstring that may have been caused by dehydration.

Getting Rodriguez out of the game likely prevented a more serious injury as there is a chance he will make his start on Sunday in Detroit.

“I think we got this early,’’ manager John Farrell said. “He was not right; he was definitely favoring it. . . . It doesn’t seem to be a significant restriction at this point.’’

Before he came out, Rodriguez struck out seven with two walks and was dominating the Orioles. His leg started to bother him in the fourth inning.

“It felt like something got tight in there,’’ Rodriguez said. “Come into the fifth inning it felt like it was getting worse. I feel like I made the right decision before it got worse.’’

Rodriguez, who has a 2.52 earned run average in his last seven starts, threw all of his pitches with precision Tuesday, challenging hitters such as Manny Machado and Mark Trumbo with his fastball and winning those battles.

“It was hard for me to come out of that game.’’ Rodriguez said.

Betts’s three-run homer in the fifth inning stood up until the seventh when the Red Sox bullpen again struggled.

With one out and a runner on first, Steve Pearce reached on an infield single against Matt Barnes to break up the no-hitter.

Lefthander Fernando Abad, obtained at the trade deadline for just this purpose, walked lefthanded-hitting Chris Davis on four pitches that were nowhere near the plate,

Abad then threw an 88-mile-per-hour cookie over the middle that Matt Wieters knocked into left field for a two-run single.

Opponents are 5 of 8 with two walks and one strikeout against Abad with runners in scoring position since the Red Sox obtained him at the trade deadline. Of the 22 he has faced, 10 have reached base.

Brad Ziegler came in and struck out J.J. Hardy. When Nolan Reimold singled to right, Betts made a strong throw to the plate to keep Davis from scoring.

Ziegler walked Adam Jones to force in the tying run but left the bases loaded by striking out Jonathan Schoop.

That was big. Facing All-Star Brad Brach in the eighth, David Ortiz singled and Betts homered to left field.

Brach had not given up a home run since June 16. But Betts is 10 of 21 with seven home runs and 13 RBIs in five games at Camden Yards this season.

“Shoot, I have no idea. Somehow it’s going over the fence,’’ Betts said. “I’m just trying to put good swings on it and enjoy it.’’

Betts has 28 home runs and 89 RBIs to go along with a .315 batting average and .926 OPS. He’s a power hitter now.

“It’s definitely weird. I’ve never been that in my life,’’ Betts said.

Bradley isn’t buying the humble routine.

“We expected it,’’ he said with a laugh. “He’s going to lie to you like always.’’

Ziegler (1-3) got two outs in the eighth inning before Ross struck out Davis with a runner on.

“Just make pitches and throw a ball with some bark,’’ Ross said.

Farrell indicated that Ross would take over the lefthanded set-up role in place of Abad.

“I’m fine with whatever,’’ Ross said. “I’m fine with facing lefties or a righty pinch hits, I feel like I match up, too, because my cutter plays there. It’s a good feeling because I can get a ground ball.’’

Craig Kimbrel pitched a drama-free ninth inning for his second save in as many days, the 21st of the season.

The Red Sox have won three games in three cities in three days and are 2-0 to start an 11-game road trip.

“It’s fun to watch the guys play like that. Mookie, he’s the best player in the game right now,’’ Ziegler said. “Everybody stops to watch him hit. To get wins like this, this can only help us moving forward.’’

Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.