Steven Wright was all smiles when he departed the eighth inning Sunday night to a standing ovation. Jim Davis/Globe Staff

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Steven Wright has pitched parts of six seasons with the Red Sox but has yet to appear in a playoff game. The knuckleballer contributed to division-winning teams in 2013, 2016, and ’17 but did not merit a spot on the postseason roster.

Wright’s best opportunity was in 2016, the year he made the All-Star team. But a shoulder injury ended his season in September.

Now the 34-year-old may have a prominent role in October coming out of the bullpen.

Wright pitched two scoreless innings in Sunday night’s 6-5 victory against the Houston Astros, stabilizing the game for the Sox after they allowed four runs in the sixth inning.

“His ability to make good hitters look bad, take bad swings — that was good,” Sox manager Alex Cora said. “He was under control. He was able to throw a lot of strikes.”

Wright threw 12 pitches in the seventh inning, all for strikes, and three more to start the eighth inning before finally missing the plate. He has pitched three times in relief since coming off the disabled list Sept. 1 and given the Sox four scoreless innings.

The increased possibility of passed balls or wild pitches requires a certain amount of courage by a manager to use a knuckleballer in relief. But Wright has pitched well for the Sox when healthy and he finally is after missing nearly 11 weeks with inflammation in his left knee.

“I feel good right now,” Wright said. “I’m not thinking about roles. I’m going to go out there when they need me to throw. I just try to go out there and throw as many strikes as I can.”

Using a knuckleballer out of the postseason bullpen is something the Red Sox have done before. Tim Wakefield pitched in 16 playoff games for the Sox from 1995-2008, seven in relief.

Wakefield pitched three scoreless innings in Game 5 of the 2004 ALCS. He also picked up five huge outs in Game 4 of the 2003 Division Series against Oakland.

Wakefield worked 3⅓ important innings in Game 3 of the 2004 ALCS, forfeiting a start the next day to save the bullpen in a lopsided loss against the Yankees. That helped lead to the history-changing comeback by the Sox.

The experience with Wakefield has convinced the Sox a knuckleballer used in relief can change the game by what his conventional pitch does to the reaction time of the hitters.

Imagine the Sox starting a game with Chris Sale, using Wright for two innings then bringing in Craig Kimbrel to close. An opposing hitter could face pitches ranging from 76 to 100 miles per hour.

Wright also has shown the ability to mix in a fastball for a strike, which he did to Tyler White in the seventh inning on Sunday.

“That was good to see. The fact he can go multiple innings is going to help us out,” Cora said.

That the bullpen badly needs help is obvious. The Red Sox had a strong group in the first half, the relievers ranking among the American League leaders in earned run average (3.27), WHIP (1.22), and strikeout-to-walk ratio (2.85).

The Sox also allowed only 28.8 percent of inherited runners to score.

But since the All-Star break, Sox relievers have a 3.91 ERA (seventh in the league), a 1.41 WHIP (12th), and a 2.30 strikeout-to-walk ratio (12th).

Since the break, the Sox have allowed 37.5 percent of inherited runners to score.

In the last six games, against two division leaders in Atlanta and Houston, Red Sox relievers allowed 13 earned runs on 21 hits over 27⅓ innings. Seven of 13 inherited runners scored.

“We’re figuring a few things out while we’re trying to win games,” Cora said.

That the Red Sox did not obtain at least one relief pitcher before the July 31 non-waiver trade deadline was a surprise at the time. That there was a need only has become more obvious in the weeks since, especially with primary set-up man Matt Barnes now unavailable to pitch because of inflammation in his left hip.

President of baseball operations Dave Dombrowski has said he did not feel any player available on the trade market represented an upgrade. He also pointed out righthander Nathan Eovaldi, a starting pitcher obtained from the Tampa Bay Rays on July 25, could move into the bullpen.

But Eovaldi has a 6.85 ERA in his last six starts with only 6.4 strikeouts per nine innings. Sale is scheduled to come off the disabled list and pitch two innings against Toronto on Tuesday night with Eovaldi to follow.

At this point, there is more evidence Wright would be an effective reliever than Eovaldi.

Wright being able to hold the Astros down on Sunday enabled the Sox to eventually win the game in the ninth inning.

“I think it’s huge. It was definitely kind of crazy,” he said. “I was trying to throw as many strikes as I could. It was a tie game against a good team and all I could do was pound the [strike] zone as much as I can.”

A willingness to throw strikes can make all the difference in relief.

“Like I said, I’ll do whatever they ask,” Wright said. “I’m healthy and ready to pitch.”