Cosart threw eight shutout innings to beat Tampa Bay once again, and rookie George Springer's two-run homer helped the Astros defeat the Rays 3-1 Friday night.
Cosart (7-5) gave up six hits in winning his third straight start. He walked one and struck out two, retiring 12 straight at one point.
The 24-year-old Cosart topped the Rays last Saturday in Houston, the Astros' last victory before losing four in a row.
The pitching matchup against Price (5-7) was a rematch of Cosart's major league debut at Tampa Bay last July 12 in which he took a no-hit bid into the seventh inning and finished with eight shutout innings and a win.
"He's a guy I've watched for years, and he's one of the best in the league and he's proven that, and that's where we're all trying to get," Cosart said. "I was trying to compete with him pitch-for-pitch, and you know he's not going to make too many mistakes. Tonight he made one, really."
After striking out in his first five at-bats against Price, including his first try Friday night, Springer hit his 13th home run off the D-ring catwalk at Tropicana Field. It came in the third inning after the first of Jose Altuve's three hits.
"I was a little bit in front of it and just didn't want to hook it," said Springer. "I was actually saying to myself: `Just stay fair!"
Price "had some success off me the last game and he still has some success off me. It was one of those things where I was just able to hit it," Springer said.
Price gave up six hits while striking out 12 in eight innings. It was his fourth straight game with double digits in strikeouts, tying Boston's Jon Lester (in 2010) for the longest such streak since 2008. Price is 1/3 in those four starts for the Rays, who have lost 18 of 24.
A second-inning strikeout of Chris Carter was the 1,000th of Price's career.
"It (the strikeout) is cool, can't deny that," Price said. "But it stinks. You want to win out there and we're not doing that right now so it's frustrating."
Altuve leads the majors with 101 hits. Batting second in front of Springer, the Houston second baseman is 11 for 18 in four games since returning from a hand injury.
"It really puts the pressure on the opposing pitcher with a guy that leads the league in hits," Astros manager Bo Porter said. "He's going to be on base a bunch, and then you have a guy in the batter's box that can change the game with one swing. It's a pretty good dynamic for our lineup."
The Astros optioned RHP Paul Clemens to Triple-A Oklahoma City and called up RHP Jake Buchanan, who will start Saturday's game against Tampa Bay RHP Jake Odorizzi. ... Price leads AL pitchers in innings (115 2-3) and strikeouts (133), along with hits (116) and home runs (16) allowed. ... With the signing of LHP Brock Burke, the Rays announced they have signed all 11 of their picks in the first 10 rounds of the draft.