DeShields, in his fourth game since returning from the disabled list and a strained left hamstring, led off the inning with a walk. He then stole second and went to third on a passed ball that didn't get far away from catcher Derek Norris.
After Shin-Soo Choo struck out, Prince Fielder hit a popup into short left-center. Third baseman Will Middlebrooks went back onto the grass to make the catch and hesitated after avoiding a collision with center fielder Melvin Upton Jr. DeShields took advantage of the hesitation and raced home to score the run.
"If the infielder caught the ball, I was going to go regardless of what happened," DeShields said. "If Upton catches it, I wasn't going because his momentum would be to home plate."
Rangers manager Jeff Banister said the play was a reminder of what speed can do at the top of a lineup.
"It allows you to manufacture runs," Banister said. "Right now, with our lineup, we need the top of the lineup to get on base and create some runs for us. When the top of the lineup gets on base, we're going to score some runs. When Delino gets on base, they have to pay attention to him as an opponent."
DeShields has started the last four games at the leadoff spot while Martin has been out of the lineup. The first two games were against left-handed starters, but the last two were against right-handers. DeShields' early playing time this season was mainly against left-handers, but now it could be against everybody.
They were both in the lineup earlier in the season, but that may not happen much if the Rangers can keep Josh Hamilton in the lineup.
The Rangers are 14-10 when DeShields bats leadoff. They average 5.25 runs per game when DeShields is in the leadoff spot and 3.84 in all other games.
"Prior to getting hurt, Delino was a catalyst," Banister said. "We're giving him an opportunity to get engaged and spark this offense. Josh coming off the disabled list, we're trying to get his bat in the lineup. Leonys is still a part of the winning process, but right now we're giving an opportunity to a guy who was playing well before he got hurt."
Martin still played, entering the game as a defensive replacement for DeShields in the eighth.