The defending AL champion Rangers scored all their runs off Verlander before the game was interrupted twice for a total of 1 hour, 50 minutes in the top of the fifth. The final out wasn't until 12:03 a.m. CDT.
"I think that this was a little bit of a weird night, obviously, with the rain the way it was," Tigers manager Jim Leyland said.
David Murphy hit an RBI triple in the second and scored on Ian Kinsler's single, and Cruz's leadoff homer in the fourth made it 3-0.
"Definitely important to get it going," Cruz said. "As soon as I hit the homer, I thought it should be good enough, the way C.J. was throwing. And with the bullpen we have, we were lucky enough for it to be enough."
In between the delays, Austin Jackson doubled in a run and scored on a wild pitch by Rangers starter C.J. Wilson. Alexi Ogando, who got all three of the Rangers' regular-season wins over Detroit this year, pitched two scoreless innings for the victory. Neftali Feliz, clocked at up to 101 mph, worked the ninth for his fourth save this postseason.
Game 2 is Sunday night. Derek Holland starts for Texas against Max Scherzer, who pitched 1 1-3 innings in relief for the Tigers in their AL division series clincher Thursday night against the New York Yankees.
Texas faced Verlander only once during the regular season, a 2-0 Rangers' win on April 11 when Verlander lost despite pitching a six-hitter.
The likely AL Cy Young Award winner was 24-5 during the regular and had been 3-0 with a 1.29 ERA in his three previous career starts at hitter-friendly Rangers Ballpark, allowing three runs in 21 innings. Texas matched that run total in four innings when it counted most.
"I thought tonight that his control was not good. His control was not very good," Leyland said. "He didn't really have his curveball going for strikes. He had a tough time with it. I think probably trying to overthrow it a little bit."
Verlander threw one inning and 25 pitches in the division series opener at Yankee Stadium on Sept. 30 when that game was suspended by rain. Under a rules change adopted two years ago, postseason games are suspended when called instead of being cut short or wiped out.
Verlander came back and started Game 3, winning as he threw 120 pitches with 11 strikeouts over eight innings, and he threw 82 pitches in four innings against the Rangers before the first delay. He struck out five, including Josh Hamilton and Adrian Beltre in the first without allowing a run after his only two walks.
Leyland said the plan was for Verlander to go back in after the first delay. That all changed when the game resumed for good about two hours after his last pitch.
"When the second (delay) came about, that was a no brainer," Leyland said. `I think that this was a little bit of a weird night, obviously."
Mike Napoli had a leadoff single in the second for the Rangers, in their second consecutive ALCS after never winning a postseason series before last year. He scored when Murphy got the head of his bat on a low pitch and pulled it into the right-center gap, where the ball one-hopped the wall.
Cruz's drive leading off the fourth ended an 0-for-10 postseason slump and was his Rangers-record seventh postseason homer, one more than two-time AL MVP Juan Gonzalez.
Before the fifth inning, Rangers Ballpark groundskeeper Dennis Klein went out and spoke with plate umpire Tim Welke about the weather. There had already been a couple of short periods of rain before then.
A few minutes later, after Ramon Santiago led off the fifth with a double and while Brandon Inge was batting with a 1-0 count against Wilson, the intensity of the rain picked up. Welke then stopped the game for the first time and had the field covered.
Play was stopped for 41 minutes but the teams got only 13 minutes in before the tarp came out again. In between the delays, the Tigers scored twice and loaded the bases with two outs.
The rain delays were the first at Rangers Ballpark since May 24. This season was played during one of the hottest and driest summers ever in North Texas, including 27 games when the temperature was 100 degrees or more at first pitch.
Wilson, who had thrown 72 pitches before the first delay, threw 24 more during the short resumption.
On the first pitch after play resumed, Inge grounded out. Jackson followed with a double that rolled into a puddle by the wall in right-center field and scored Santiago. Jackson eventually scored on a wild pitch while Wilson loaded the bases on three walks before heavy rain started falling again.
Michael Gonzalez replaced Wilson and needed only two pitches to induce an inning-ending groundout by Alex Avila.
Ogando, a reliver-turned-starter who is back in the bullpen in the playoffs, struck out three over the sixth and seventh innings. While he was beating the Tigers during the regular season, the other Rangers pitchers combined to go 0-6.
"What a weapon to have," Rangers manager Ron Washington said.
When Jackson struck out to end the sixth, Ogando hopped off the mound slapping his glove. He had a similar reaction when Martinez struck out to end the seventh.
Santiago led off the ninth with a bunt single before Feliz struck out the next three batters.
Rick Porcello, Detroit's scheduled Game 4 starter, had two scoreless innings after replacing Verlander. Leyland said the Tigers could alter their planned rotation for the rest of the series.
Ryan Raburn and Miguel Cabrera had consecutive sharp singles to left after Austin Jackson took a called third strike leading off the game. Raburn was playing left field and AL batting champion Cabrera batting third for only the second time this season after slugger Delmon Young was left off the ALCS roster because of an oblique injury on his left side.
Victor Martinez drew a walk on a full-count pitch that missed badly, Wilson escaped the first without giving up a run when Magglio Ordonez hit a chopper over third base. Adrian Beltre stepped on the bag and threw across the diamond for an inning-ending double play.
"The first inning was probably a huge key. We loaded the bases, and C.J. made a great pitch on Magglio, cut a fastball in," Leyland said. "That was obviously a huge inning. The ninth inning we always talk about, but tonight's game might have been the first inning -- the first was a huge inning for us."
The Tigers again had consecutive one-out singles in the second, again without scoring.
Raburn had a leadoff walk in the third. Then after Cabrera took a called third strike, Martinez hit into another double play started by Beltre -- the slick-fielding All-Star who in the AL division series clincher against Tampa Bay became only the seventh player ever to hit three homers in a postseason game.
Wilson struck out all three batters faced in the fourth before running into trouble in the wet and twice-delayed fifth.
NOTES: This was the ninth one-run game already in this postseason, the most since there were 11 two years ago, according to STATS LLC. ... Jackson, who was born and still lives in nearby Denton, had a tough start. After striking out on three pitches opening the game, he struggled with a wind-blown flyball in the bottom of the first. He went back, came in a few steps and the ball hit off the heel of Jackson's glove as Elvis Andrus reached second on the error.