ATLANTA — Adam Duvall swung and the baseball sailed high and deep and, surely, toward the history books. The 43,122 Atlanta fans filling Truist Park, early arrivals and in the mood to party with a clinching World Series win within reach, exploded into a raucous din. They believed the grand slam, only the 21st in World Series history, signaled their divine right to celebrate.

It was the first inning.

The Houston Astros are here for a reason, too, although they hadn’t exhibited it much lately. But they finally found their offensive groove just when they needed it, facing elimination in Game 5. A shake-up in the lineup and a big day by a light-hitting catcher produced a series-saving 9-5 victory for the Astros.

It had been a tough few days for the Astros. They hadn’t played in Atlanta since 2017 and, because of cold and rainy conditions, not only was their planned workout on Thursday evening canceled, but pregame on-field batting practice before Games 3 and 4 were wiped out, too. So the only time the Astros were on the unfamiliar field was during the games themselves.

Offensively, it showed. They scored only two runs over the first 18 innings here, losing games 2-0 and 3-2 and having a terrible time throughout. Including the games in Houston, the Astros were 4 for 31 with runners in scoring position in the series.

But Manager Dusty Baker stubbornly said “I believe in miracles” before Game 5 and, while perhaps the comeback his team was facing might not quite qualify, maybe he was onto something given the futility with runners in scoring position. Houston had left 17 runners on base during the first two games in Atlanta.

One fact Baker cited before Game 5 was that as recently as the 2016 World Series, the Chicago Cubs trailed Cleveland three games to one but came back to win the title.

Houston’s offense woke up, finally, on Sunday when the skies cleared and the area dried. The Astros scheduled some early work on the field for midafternoon, before Atlanta’s batting practice session. Whether that alone brought change, or whether the Astros’ hitters are simply too good to be held down for long, things changed dramatically in Game 5.

Down by 4-0 early, Houston scratched across two runs in the second when Yuli Gurriel drove a one-out single to center, Kyle Tucker walked and Alex Bregman, struggling so badly that Baker dropped him to seventh in the lineup, knocked an R.B.I. double. Tucker then scored on catcher Martín Maldonado’s fly ball to center field.

It was a beginning. The Astros tied it, 4-4, with two more runs in the third. Atlanta shortstop Dansby Swanson booted a ground ball to give Houston a start there. Then the Astros shook off a Freddie Freeman homer that briefly put Atlanta on top, 5-4, by scoring three more times in the fifth. Carlos Correa and Yuli Gurriel rapped base hits, Bregman was intentionally walked with two outs and first base open and Maldonado, again, followed by working a clutch, bases-loaded walk against Atlanta reliever A.J. Minter.

Maldonado, the defensive stalwart at catcher who typically contributes little offensively, had drawn just one walk in 47 plate appearances this postseason at the time. But on a night when Houston was desperate for help from all corners of its roster, Maldonado stepped up. The player who finished with the worst batting average during the regular season of all big league catchers with at least 400 plate appearances (.172) finished with three R.B.I., the third coming on a base hit in the seventh two batters after a Tucker double.

Correa chipped in an R.B.I. single in the eighth that was an unnecessary, but welcome, insurance run.

It all wiped out the Duvall grand slam that so many here figured was a sure sign that Atlanta was going to clinch its first World Series title since 1995. It was the first World Series grand slam in the first inning since the Yankees’ Bobby Richardson hit one in the 1960 World Series.

That, and the fact that Atlanta was a perfect 7-0 at home this postseason, seemed to be premonitions for a big celebration in this town overnight Sunday. Instead, the World Series now will move back to Houston for Game 6 on Tuesday night, with the Astros’ offense showing signs of life and at least some indication that, perhaps, there may be a long way to go yet in this series.