With the single off Tigers reliever Victor Alcantara, Choo surpassed the team record of 46 straight games set by Julio Franco in 1993.
Choo grounded into a double play to end the top of the seventh inning but held out hope that he'd get another trip to the plate. Choo had reached on an error in the second inning but hadn't reached via a hit or walk in his four plate appearances.
"I still believed I'd get another at-bat,'' Choo said.
His teammates rewarded that belief, as the Rangers sent five men to the plate in the eighth, and Ronald Guzman's one-out single in the ninth allowed Choo to bat again.
He hit a slow grounder to third and made it to first without a throw.
"I don't know how I did it -- 47 games already,'' Choo said. "A lot of people helped, especially my teammates.''
Choo has been serving as the team's DH while recovering from a strained right quadriceps that the team has said will limit him defensively for a few weeks.
For the season, Choo is hitting .293 with 17 home runs and 42 RBIs.
Information from The Associated Press was used in this report.