During a nine-pitch at-bat, Olt fouled off four pitches and checked his swing on a curveball in the dirt. The 23-year-old Olt then drove a 2-2 pitch from Phil Coke past diving third baseman Miguel Cabrera into left field to score Cruz, who easily beat the throw home.
Olt, one of the Rangers' most highly touted prospects, was called up on Aug. 1 after belting 28 home runs in Double-A Frisco. The right-hander batted for Mitch Moreland against the left-handed Coke.
"It's been a surreal experience," Olt said. "It's been a special week. It's good to get in there and get my feet wet."
Olt was mobbed by his teammates in a wild celebration near first base after he became the first Rangers rookie with a game-ending pinch hit since Mike Lamb did it on May 5, 2000.
"For a young kid, he looked calm to me," Rangers manager Ron Washington said. "He didn't look overwhelmed."
The Rangers, who started a run on Friday of 20 games in 20 days, remained 5½ games ahead of Oakland in the AL West.
"We are playing well," Young said. "Hopefully this will give us momentum. We're in a stretch where we're playing some good teams."
Mike Adams (2-3) escaped a bases-loaded, one-out jam in the top of the ninth to earn the victory. Cabrera was forced out at home on Brennan Boesch's slow grounder to first. Jhonny Peralta lined out to center to end Detroit's threat.
"We didn't get a run in from third," Tigers manager Jim Leyland said. "That cost us two games in the last three days. I'm not mad or upset about it. That's just the way it is."
Holland tied a season-high with nine strikeouts in 7 2/3 innings. The left-hander allowed three hits and walked one.
Holland was 1-2 with a 7.00 ERA in his previous four starts. He got off to a rocky start when Jackson homered on the fourth pitch of the game and Omar Infante followed with a single.
After that, Holland allowed only a walk to Cabrera in the fourth and Peralta's single in the fifth.
"(Holland) stood up for us," Washington said. "He was competing hard. He did what he had to do."
Verlander allowed seven hits and one run in seven innings. The reigning AL MVP struck out eight in a 118-pitch outing.
Verlander, who retired the final 10 batters he faced, leads the majors with 174 strikeouts.
Jackson homered on a 1-2 pitch leading off the game. It was Jackson's ninth career leadoff blast and fifth this season.
The Rangers had three consecutive singles with two outs in the third. Cruz's broken bat RBI hit capped the rally and tied the game at 1.
The Rangers celebrated their 40th anniversary in Texas by honoring their all-time team and inducting radio broadcaster Eric Nadel into the team's Hall of Fame in a pregame ceremony. Both teams wore their 1976 uniforms as part of the celebration. ... Detroit's Rick Porcello (9-6) will face Texas rookie Yu Darvish (11-8) in the series finale Sunday. ... Texas RHP Koji Uehara, who has been on the disabled list since June 10 with a right lat strain, will throw a bullpen session on Sunday.