Astros manager Dusty Baker tested positive for COVID-19 prior to the game. Baker held his usual pregame availability with the media about two hours before the 7:10 p.m. first pitch.
Baker, 73, is in his third season as Houston's manager. Bench coach Joe Espada filled in for Baker against Cleveland.
Mancini, acquired from Baltimore on Monday to bolster Houston's already dynamic lineup, hit a solo homer in the second and capped the Astros' five-run third with a blast that cleared the 19-foot wall in left field and landed in the home run porch.
"It took me a long time," Mancini said about his grand slam. "I finally got one."
Mancini, starting at DH on Friday, has homered three times in four games with Houston. The Astros acquired him in a three-team trade that also included Tampa Bay.
Mancini missed the 2020 season while battling Stage 3 colon cancer. He returned to the field last season and was named the AL Player of the Year. Mancini batted .268 with 10 home runs and 41 RBI with Baltimore this season.
Mancini said he spent the first day with the Astros learning the names of his new teammates and is feeling more settled.
"From the second I got traded here I just wanted to make a positive impact whenever I'm in there," he said. "Hopefully I can keep it going."
Yordan Álvarez drove in his 73rd run of the season - good for third in the AL - with a single in the third inning that gave Houston a 2-1 lead. Jose Altuve had three hits and an RBI.
Valdez was pulled after walking rookie Will Benson to load the bases with one out. Seth Martinez retired Rosario on a popup and struck out pinch-hitter Nolan Jones. Valdez allowed three runs and seven hits in 6 1/3 innings.
Houston has won seven straight at Progressive Field and has outscored Cleveland in the first two games of this series 15-3.
Mancini and the Astros spoiled the major league debut of Cleveland right-hander Hunter Gaddis (0-1), who was charged with eight runs in 3 1/3 innings. He retired the side in order in the first before Houston's offense took control.
Gaddis became the 13th Cleveland player to make his major league debut this season. He was 5-3 with a 4.07 ERA in 17 games with Double-A Akron and Triple-A Columbus. Cleveland selected Gaddis, 24, in the fifth round of the 2019 draft.
Mancini's one-out homer in the second tied the game. Houston strung together three singles and a walk before Mancini's grand slam in the third that came on a 3-1 pitch.
"I never had three guys waiting for me that were on base before so it was a really good feeling," he said.
Cleveland rookie Steven Kwan was 0 for 2, snapping his 18-game hitting streak. Kwan was removed from the game in the fourth inning after fouling a pitch off his leg in the first.
THINKING OF DUSTY
Espada said no one else with the Astros has been affected by COVID-19 as of the conclusion of Friday's game.
Guardians manager Terry Francona sent his best wishes to Baker.
"Ya know we didn't find out until about the fifth inning," he said. "I knew Dusty wasn't there. I hope he's OK. I mean, man, he's near and dear to everybody. He's so much of what's good in baseball. I hope it just feels like he has the flu or an allergy and is back because we care about him."
Gaddis was told around 10 p.m. Thursday that he would be pitching in the big leagues in less than 24 hours.
"It was crazy," he said. "I blacked out. I don't remember the conversations I had, for the most part. I was just rushing around, trying to get everything together. It was amazing, I can tell you that."
Astros: Baker said before the game that tests on OF Aledmys Diaz's left ring finger showed no fracture. Diaz, injured after colliding with center fielder Jake Meyers on a fly ball Thursday night, was out of the lineup. ... OF Kyle Tucker, missed his second straight game with an illness.
Guardians: RHP Aaron Civale (right wrist sprain) allowed two runs (one earned) in four innings on a rehab start for Triple-A Columbus on Friday. He has been on the 15-day injured list since July 14.
Astros: RHP Luis Garcia (8-7, 3.81 ERA) got the loss against Cleveland on May 23, allowing four runs - two earned - over five innings.
Guardians: RHP Cal Quantrill (7-5, 4.08 ERA) lost to the Astros in Houston on May 25. He gave up two runs, six hits and four walks in six innings.