A win Friday night, however, would extend the Houston Astros' losing streak to their longest in franchise history.
New York hits the road looking to hand Houston its 13th consecutive defeat.
The Yankees (82-77) continue to limp to the finish following a 4-0 home loss to Tampa Bay on Thursday, completing a three-game sweep in which they were outscored 19-3. It was also their ninth loss in 12 contests.
But Rivera's final home appearance provided a highlight in what has been a roller-coaster year for the Yankees.
Rivera, who came on in the eighth with one out, retired all four batters he faced before teammates Derek Jeter and Andy Pettitte came to the mound to remove him instead of manager Joe Girardi, setting the stage for an emotional farewell.
"I was bombarded with emotions and feelings," Rivera said. "Everything hit. I knew that's the last time. Period."
Houston has planned a pregame ceremony for Sunday's contest that will include former Yankees manager Joe Torre as well as Roger Clemens. Rivera has thrown 5 1-3 shutout innings over six career appearances against the Astros, converting all five save opportunities.
Girardi said prior to Thursday's game that he may let Rivera play center field for an inning during the series.
"In my mind, thinking that he's going to want to pitch, it would be a situation that I might bring him in (in) the eighth to play the outfield and close him out in the ninth if we have that opportunity," Girardi said.
Before honoring Rivera, however, the Astros (51-108) are trying to avoid what would be the longest losing streak in club history. While the Yankees have struggled lately, they're 10-2 all-time against Houston and took two of three in New York from April 29-May 1.
Houston's 7-3 defeat at Texas on Wednesday established a single-season franchise record for losses and baseball's most since 111 by Arizona in 2004.
"It's not fun at all. We go out there and want to win, but it's not happening. We're going to have to fix things and come back stronger next year," center fielder Brandon Barnes said. "I believe in the guys in this clubhouse, and there are guys coming up who can do the job."
Rookie left-hander Brett Oberholtzer (4-4, 2.71 ERA) figures to give the Astros a chance, though he'll need more offense behind him. He's lost his last three starts despite a 2.50 ERA, receiving three runs of support over 18 innings.
His last defeat - in a 2-1 final at Cleveland last Friday - came despite the fact that he didn't surrender an earned run in six innings. Instead, three errors contributed to two unearned runs.
"If we made a couple of defensive plays, we arguably could be standing here with a 1-0 victory," manager Bo Porter told the team's official website. "He pitched that well. He continues to grind and make pitches and give us big performances."
The Yankees have yet to name a starter since moving Pettitte's scheduled start to Saturday.
Ichiro Suzuki is batting .460 in 11 career games against the Astros and went 5 for 9 in two meetings earlier this year.