The Texas right-handers were two of five bright spots for a bullpen that bailed out rookie starter Justin Grimm on Sunday.
"This bullpen deserves all the credit today," Pierzynski said.
Each reliever pitched a scoreless inning apiece, starting with Burns when he escaped a jam with runners on first and third and no outs in the fifth.
Closer Joe Nathan pitched a perfect ninth for his 29th save in 30 chances a day after making his sixth All-Star team and second in two seasons with Texas.
It was Soria's first big league appearance since Sept. 11, 2011, when the two-time All-Star with 160 career saves was the closer for the Kansas City Royals before getting shut down by elbow reconstruction surgery.
"I've been working really hard so it was no time to doubt myself or get nervous," Soria said. "Everything I've worked for is here now, and I'm just going to enjoy it."
"He looked like he hadn't missed a day," said Pierzynski, the Texas catcher who watched the steady parade of relievers. "Most guys that haven't pitched in over a year are a little nervous, a little fidgety out there. He was like, `Ho hum, another spring training game."
Krauss answered with his first career homer in the second, a two-run shot off Grimm.
Cruz's single scored Ian Kinsler for a 5-4 lead after Houston had pulled even in a fifth inning that included three errors, two unearned runs and two unusual double plays.
"I felt like we had some chances offensively," Houston manager Bo Porter said. "We just weren't able to come up with the big hit."
The Rangers had Barnes picked off at third, but Jurickson Profar -- filling in for Gold Glove third baseman Adrian Beltre -- let Pierzynski's throw from behind the plate sail past his glove into left field. Profar got the error, and Barnes scored for a 4-all tie.
Grimm was replaced after a walk to No. 9 hitter Jake Elmore, and Cory Burns retired Jose Altuve on a pop out. Burns escaped the inning when Brett Wallace struck out and Elmore was tagged out by shortstop Elvis Andrus on a steal attempt after sliding past the bag at second.
Burns was called up from Triple-A Round Rock and made the 2 1/2-hour drive to the Dallas area Sunday morning. Then he found himself in a sticky situation.
"But that's what the bullpen is for," said Burns, who had an 0-1 career record with 17 appearances in San Diego and three in an earlier Texas stint. "That's what we trained for all through the minor leagues is to come into those type of situations."
Altuve botched a routine grounder from Kinsler to start the Texas fifth. After Andrus walked, Kinsler scored for a 5-4 Texas lead on a single from Cruz, who was later thrown out trying to go to second on a deep flyout to center field by Pierzynski.
"I'm just glad the two mistakes we made didn't cost us anything but a tie game, and we were able to put a run on the board and win it," Rangers manager Ron Washington said.
J.D. Martinez had three singles for Houston but never made it to second base. He was picked off by Grimm to end the fourth after driving in Corporan to pull Houston to 4-3.
The Rangers put DH Lance Berkman (left hip inflammation) and RHP Nick Tepesch (right elbow inflammation) on the disabled list. Soria was reinstated from the 60-day DL, and RHP Cory Burns was called up from Triple-A Round Rock. ... The Astros are moving RHP Lucas Harrell to the bullpen. He is 5-9 with a 5.04 ERA after giving up nine runs (seven earned) in 3 2/3 innings in a 10-5 loss to the Rangers on Friday. A replacement hasn't been announced. ... The Texas-Arizona game that was postponed by rain on May 29 will be made up Aug. 1. It was a scheduled off-day for both teams.