Price allowed three hits, struck out seven and walked three in his first game at Comerica Park since he was acquired in a trade with Tampa Bay last month.
Rick Porcello struggled badly in his first appearance since pitching the final three innings of Detroit’s 19-inning loss in Toronto on Sunday.
A former home of baseball’s Negro Leagues has been recognized with a historical marker.
The loss, coupled with Kansas City’s 3-2 win over Oakland, dropped the Tigers a half-game behind the now first-place Royals in the AL Central Division.
Danny Valencia singled off Joba Chamberlain to begin the 10th and Reimold followed with a double to the wall in left-center as Valencia scored without a play.
The rookies knocked back-to-back jacks off of Toronto closer Casey Janssen after Tigers starter Anibal Sanchez left with an injury in the fifth inning.
Detroit’s trainer came to the mound and could be seen massaging the area around Sanchez’s armpit.
The Tigers scored just one run on six hits to back up reigning Cy Young winner, Max Scherzer.
Newly called-up center fielder Ezequiel Carrera will get the nod from manager Brad Ausmus in Monday’s opener against the Yankees in New York.
The 28-year-old Price said he knew there was a good chance Tampa Bay would deal him before the trade deadline.