HOUSTON -- On Sunday, Texas Rangers left-hander Jordan Montgomery earned the distinction of being just the third pitcher in franchise history with multiple Game 1 starts in the postseason, and he delivered a performance worthy of that footnote in club annals.

Montgomery carried a shutout into the seventh inning and Leody Taveras socked his first career playoff homer as Texas extended its franchise-record postseason winning streak to six games with a 2-0 victory over the Houston Astros in Game 1 of the American League Championship Series.

The Rangers will look to run that winning streak to seven games, and claim a 2-0 lead in the series, on Monday in Houston.

Montgomery (2-0) improved to 4-0 with a 1.22 ERA over his last seven starts (regular and postseason) by limiting the Astros to five hits and one walk with six strikeouts over 6 1/3 innings.

A trade deadline acquisition from the St. Louis Cardinals on July 30, Montgomery previously worked seven shutout innings in a 4-0 victory in Game 1 of the AL wild-card series against the Tampa Bay Rays. He joined fellow lefties C.J. Wilson and Cliff Lee in making multiple Game 1 postseason starts for the Rangers.

"If it doesn't raise your game in the playoffs, I don't think you're doing it right," Montgomery said of the opportunity to start in the postseason. "Obviously I'm super excited to take the ball (Sunday). And anytime I can give my team a chance to win, I'll do my best."

Taveras finished 2-for-2 with a walk batting in the nine-hole against Astros right-hander Justin Verlander. He drilled a 1-2 slider from Verlander 398 feet into the right field seats with one out in the fifth to double the Rangers' lead.

Texas had grabbed a 1-0 advantage off Verlander (1-1) in the second when Jonah Heim followed a one-out double by Evan Carter with an RBI single.

Verlander gave up two runs on six hits in 6 2/3 innings. He walked two and fanned five.

Carter, a 21-year-old rookie, started a critical double play in the eighth when he fielded a deep fly ball from Alex Bregman in the left-center-field gap before firing a throw in to shortstop Corey Seager, who followed with a throw to second baseman Marcus Semien.

Jose Altuve, who walked leading off the inning, failed to touch second base when he rounded the bag and returned to first on the Bregman flyout. Altuve was ruled out after the Rangers challenged the initial call.

"I thought it would be a low-scoring game," Texas manager Bruce Bochy said. "Our guys played well. Our defense was outstanding (Sunday). The kid Carter, what a game he had out there."

Montgomery faced just one batter over the minimum through two innings before running into a spot of trouble in both the third and fourth. It was the ability to record timely strikeouts that proved critical for Montgomery when the Astros created traffic on the bases trailing by one run.

Montgomery dominated his matchup with Astros left-handed slugger Yordan Alvarez, recording inning-ending strikeouts of Alvarez in the first, third and fifth innings. Alvarez swung over a 3-2 curveball in the third after Bregman stroked a single to left that advanced Martin Maldonado to second base.

After recording two quick outs to open the fourth, Montgomery surrendered three successive singles to load the bases for Maldonado, who promptly struck out on a four-seam fastball to mute that threat.

Montgomery then executed a timely pivot back to his dominating form, retiring the Astros in order in the fifth and sixth innings on just 18 pitches.

"They say good pitching beats good hitting, but when you don't hit, everybody wants to know what's wrong," Astros manager Dusty Baker said. "There's not a whole bunch to say. (Montgomery) threw a real good game against us."

Jose Leclerc retired the Astros in order in the ninth for his second save as Texas claimed its sixth consecutive postseason win.

--MK Bower, Field Level Media