BALTIMORE — As the Red Sox push aside division opponents and check days off the calendar, the construction of their postseason roster is an increasingly important topic.
Specifically, which starter would draw the third game of the division series on Oct. 9?
David Price and Rick Porcello are the obvious choices to start the first two games. But the Sox have not had a clear No. 3 starter since Steven Wright injured his shoulder while running the bases in early August.
Drew Pomeranz was a candidate before pitching poorly in his last two starts. He looks worn down as his first full season as a starter in the majors nears the end.
Clay Buchholz doesn’t quite fit the profile, even with his recent success.
That leaves Eduardo Rodriguez, who on Tuesday night showed just how badly he wants that important job.
The lefthander worked into the seventh inning as the Sox extended their win streak to six games with a 5-2 victory against the Baltimore Orioles.
David Ortiz’s three-run homer in the seventh inning boosted the Sox to a five-game lead on the Orioles with 11 to play. Mookie Betts was 3 for 5, giving him 201 hits on the season.
Beyond the standings, the value of this game was the step forward taken by Rodriguez.
The 23-year-old is 3-7 with a 4.84 earned run average on the season, decidedly unimpressive.
But Rodriguez has been a different pitcher since being demoted to the minors in June and returning after the All-Star break. Adding a slider improved his ability to sequence pitches and Rodriguez has a 3.21 ERA since.
“It’s been like making a major deadline trade for us,’’ manager John Farrell said. “His renewed confidence has gone a long way. No one questioned the talent, it was a matter of putting it together.’’
Facing a Baltimore team trying to cling to a wild-card spot, Rodriguez allowed two runs on four hits and struck out seven without a walk.
“That was good. It’s going to build his confidence. We know what we have in him. He has good stuff,’’ Ortiz said. “When you are capable to stop the Baltimore offense, that means you have good stuff.’’
Rodriguez, a former Orioles prospect, no-hit Baltimore for four innings at Camden Yards on Aug. 16 before leaving the game with tightness in his left hamstring.
In his return, Rodriguez took a no-hitter into the fifth inning before Trey Mancini, playing in his first major league game, homered with two outs.
With the Sox up 2-1, Chris Davis singled for the Orioles with one out in the sixth. Mark Trumbo came up with two outs and first base open.
Trumbo leads the majors with 43 home runs and Rodriguez was careful not to challenge him in what turned into a long, tension-filled at-bat.
The first six pitches were above the strike zone, Trumbo missing one and fouling off three others.
A slider down and in was taken to load the count. Rodriguez then threw a tumbling changeup down and away that Trumbo flailed at.
Rodriguez pumped his fist as he came off the mound.
“You know how good a hitter he is. If you miss your spot, he’s going to hit a homer,’’ Rodriguez said. “Just tried not to throw a pitch for a strike and let him take a walk. But he swung and I got the out. I was excited for that.’’
Rodriguez left the game with a runner on second and one out in the seventh inning. Matt Barnes got the second out but J.J Hardy reached on an infield hit that scored Schoop.
Brad Ziegler, Koji Uehara, and Craig Kimbrel recorded the final eight outs. It was the 28th save for Kimbrel. The Red Sox bullpen has a 0.89 ERA in September.
No Sox starter is on the level of Porcello and Price. But Rodriguez has presented himself as a reliable wingman
“If they give me the chance, I’ll take it,’’ Rodriguez said.
He may well get it.
“Whoever that’s going to be, tonight was a major step forward for Eddie regardless of what takes place,’’ Farrell said. “When you look at that kind of stuff. He can get good major league hitters in the strike zone without trying to induce chase. That’s a strong ingredient as you go deeper in the season.’’
Baltimore starter Kevin Gausman threw eight shutout innings against the Sox last Wednesday. He gave up five runs in the rematch.
Betts singled to lead off the third inning, went to third on a single by Ortiz and scored when Hanley Ramirez grounded into a force. Ramirez has 107 RBIs, a career best.
Jackie Bradley Jr. homered in the fourth inning, his 26th of the season.
“Not too shabby for a defensive specialist,’’ Bradley said.
The game got much less complicated for Rodriguez in the seventh inning thanks to Ortiz’s three-run homer to center.
He strolled a few steps toward first base to admire the majestic shot. It was Ortiz’s 539th career home run, No. 36 this season. The many Sox fans in the crowd of 20,387 gave Ortiz a standing ovation.
Ortiz now has the most home runs for a player in his final season.
“I’ll try and hit a couple of more so nobody can reach me,’’ he said.
Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.
