The Braves have a 3-1 edge in the series against the Houston Astros and are looking to clinch it with a win at home Sunday night.
Davidson, 25, had a 3.60 ERA in four big league starts this season, all in May and June, after making his debut in the majors in 2020. He was 2-2 with a 1.17 ERA in four starts at Triple-A Gwinnett, making his last appearance on Oct. 3. He missed much of the season with left forearm inflammation.
Davidson has not appeared in any major league postseason games.
Morton suffered a broken fibula after he was struck on the lower right leg by a comebacker in the second inning of Atlanta's 6-2 win in Game 1 on Tuesday.
Framber Valdez, who gave up five runs in just two innings in Game 1, will again take the mound for the Astros.
"We've had our backs to the wall before," Astros manager Dusty Baker said after Saturday's 3-2 loss in Game 4. "Our guys know what to do. There's not a whole lot to be said. We know what we have to do."
The Associated Press contributed to this report.