After losses in the first two games left the Red Sox hoping to avoid a sweep, Hanley Ramirez cheered up the Fenway Park crowd by waving a "Believe in Boston" flag during introductions. He then delivered four hits and three RBIs to help the Red Sox snap a five-game postseason losing streak.
Mitch Moreland had three hits and Jackie Bradley Jr. hit his first postseason homer, a three-run shot in a six-run seventh that helped Boston pull away.
Game 4 is Monday in Boston. Houston right-hander Charlie Morton is expected to start against reigning AL Cy Young Award winner Rick Porcello.
After winning each of the first two games 8-2, the Astros took a first-inning lead for the third straight game. Up 3-0 with two on and one out in the second, Joe Kelly relieved Doug Fister and retired George Springer before Josh Reddick hit a long fly ball to right field that Mookie Betts caught at the top of the short wall to end the inning.
Kelly pitched the third and then Price turned in his seventh straight scoreless appearance since going to the bullpen in September after missing most of the season with left elbow problems.
Astros starter Brad Peacock escaped the second inning with a 3-1 lead despite loading the bases with nobody out, but he ran into bigger trouble in the third.
After Peacock struck out Boston's No. 3 and 4 hitters, Andrew Benintendi and Mookie Betts, Moreland doubled and scored on Ramirez's line drive over left fielder Marwin Gonzalez's outstretched glove. Francisco Liriano gave up Devers' two-run homer to right that gave Boston a 4-3 lead - its first in 44 postseason innings dating to Game 1 of the 2016 ALDS.
Devers, who turns 21 on Oct. 24, is the youngest Red Sox player to homer in the postseason and one of only six players in major league history to hit a postseason home run before their 21st birthday.
Ramirez drove in two more runs in a six-run seventh inning highlighted by Bradley's homer that bounced off Reddick's glove and into the stands behind the Pesky Pole.
Price allowed four hits and a walk. He exchanged words with Gonzalez after striking him out with a 95 mph fastball to end the seventh, and home plate umpire Ted Barrett walked toward the Red Sox dugout with catcher Sandy Leon to calm things down.
Peacock allowed three runs and six hits in 2 2/3 innings. Liriano got just one out while allowing one run and two hits for the Astros, who have never swept a postseason series.
Houston reliever Lance McCullers took a hard comebacker off his ankle in the fourth, but needed only one warmup pitch to test it and stay in the game.
Astros: Morton was 14-7 with a 3.62 ERA in the regular season.
Red Sox: A year after leading the league with 22 wins and winning the Cy Young Award, Porcello had a 4.65 ERA and a league-leading 17 losses.
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