The speedy leadoff hitter reached on a two-out error in the seventh, and then scored from first on a single to shallow right by Shin-Soo Choo. Jurickson Profar followed with a tiebreaking triple as the Rangers beat the Detroit Tigers 7-6 on Monday night.
"I don't really care how I get on base as long as I get on base. I know good things can happen," DeShields said. "Take advantage of their mistakes, and I'm the wrong guy to make a mistake on."
DeShields also had a leadoff walk in Texas' four-run sixth, which ended with the Rangers scoring on four straight two-out hits.
"I was taught really young, God gave me the ability to run. That should never not show up," he said. "And I just love touching home plate."
After blowing a 5-1 lead, Detroit went ahead again with an unearned run in the top of the seventh after a replay review, the first of two overturned calls after manager challenges.
First base umpire Bill Miller ruled a foul ball, but manager Ron Gardenhire challenged the call and the replay showed Mazara was clearly in fair territory. Jones was awarded home to make it 6-5, and Iglesias took first on what became an error for Mazara.
"We had a lead with (Michael) Fulmer, and just couldn't hold it," Gardenhire said. "The rest of it was we missed plays the rest of the night. We just didn't make the plays we need to make. ... Yes, we're a little disappointed."
In the bottom of the seventh, shortstop Iglesias fielded DeShields' chopper up the middle, but bobbled it briefly before making a clean throw. That was all the time DeShields needed to make it to first, and then second baseman Dixon Machado couldn't get enough of Choo's roller that trickled off his glove.
Texas won a replay challenge in the eighth when Isiah Kiner-Falefa was initially ruled off the bag on a double play. On replay, the rookie second baseman's toe appeared to barely drag across the top of the base when he caught a throw before making the relay to first. That ended the inning instead of Detroit having runners on second and third.
"The replay challenge was the key for us in that situation ... Kiner did the yard work there staying on the bag, the tough catch and it was a tough throw to first base," manager Jeff Banister said.
Leonys Martin, whose career started with Texas from 2011-15, hit his fifth homer. Detroit's leadoff hitter also doubled and scored another run. ... Mazara homered for the fifth time in May, and eighth time overall, when went deep to start the second.
Both starters allowed five runs over 5 2/3 innings. Fulmer struck out seven, walked three and allowed four hits. Rangers lefty Matt Moore permitted nine hits and walked two.
Twins: 1B Miguel Cabrera jogged in the outfield for the first time since he strained his right hamstring Thursday and went on the 10-day disabled list. "He's getting anxious," Gardenhire said. Cabrera still has another week before he can come off the DL.
Rangers: Drew Robinson was in the original lineup to play second base, but was scratched and placed on the 10-day DL because of left hip soreness. ... 3B Adrian Beltre, who missed his 12th game while on the DL with a left hamstring strain, took some swings and groundballs, and ran the bases. "He's progressing nicely," Banister said.
Rangers lefty Mike Minor (3-1), a full-time reliever for Kansas City last season after missing two full seasons with shoulder issues, makes his first start for Texas on regular four days' rest. Tigers starter Mike Fiers (2-2, 5.00 ERA) is 0-3 with an 8.90 ERA in his six previous appearances (five starts) against Texas.
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