And the Rays, despite a slumping stretch, are going home still with the best record in the majors after avoiding a weekend sweep with a 9-5 marathon victory over the AL West-leading Rangers on Sunday.
"We were all dripping. That was an excruciating game regarding the elements," Rays manager Joe Maddon said. "The weather was so good that it was bad. I'm really proud of the way we handled these last couple of days."
It took 4 hours, 6 minutes to play nine innings with the temperature in the low 90s the entire time. That was after another game in bright sunshine Saturday when it was even hotter.
A day after becoming the first Rays catcher ever to lead off, Jaso batted first as the designated hitter. He drove in a career-best five runs and had three hits to help Garza (6-4) win for the first time in a month.
Carlos Pena also homered for Tampa Bay (37-20), which has a two-game lead over the New York Yankees in the AL East. The Rays had a season-best gap of six games in the division before their current 5-8 stretch, though they broke even on the six-game trip and have a majors-best 22 road wins.
"It was great to win at the end of the road trip," Jaso said. "It lifts your spirits going home."
Tampa Bay plays 19 of its next 31 games before the All-Star break at Tropicana Field.
Jaso had a two-run homer, a two-run single and an RBI double. He even provided a lighthearted moment during the long day when he fell down making a wide turn of second base in the fifth, then was easily thrown out trying to advance.
"I blew a flat tire out there," he said. "Everybody was laughing."
Garza threw 108 pitches, allowing four runs over 5 2-3 innings. The big right-hander was 0-3 his previous five starts since May 5, when he reached five victories faster than any pitcher in Rays history.
B.J. Upton scored three runs and had three hits, with another hit taken away by a scoring change. Upton's RBI single in the sixth gave the Rays a 5-3 lead.
"I've got to credit B.J.," Jaso said. "He kept things going the whole game."
Upton raised his batting average 11 points -- still only .229 with 56 strikeouts in 55 games -- with his first three-hit game this season.
"I've been getting better and better," Upton said. "I can't press too much and I've got to let my ability take over."
Matt Treanor hit a pair of solo homers for Texas.
Texas starter Rich Harden (3-2) lost for the first time in seven weeks, though the right-hander has been less than impressive in his nine starts since losing at Yankee Stadium on April 18.
Harden threw 111 pitches and allowed four runs, three earned, with six strikeouts over five innings. The Rangers' top free-agent acquisition last winter, with a contract that guarantees him $7.5 million this season, Harden has pitched 5 1-3 innings or less in six consecutive starts.
"He's making pitches and they kept fouling them off," manager Ron Washington said. "But he's still got to figure out a way to get deeper in the game."
Garza struck out four and walked two to snap a three-game losing streak that matched the longest in his career.
The Rays never trailed after Jaso's third homer made it 2-1 in the third. Upton was on base after an error by third baseman Michael Young, a play initially ruled a base hit before being changed by the official scorer three innings later.
Pena snapped a 5-for-51 slump with his ninth homer leading off the fourth.
After Upton's leadoff double in the fifth, Jaso reached when shortstop Elvis Andrus dropped a popup in the middle of the infield. Evan Longoria's RBI single then made it 4-2 before Harden left.
"I still felt really strong," Harden said. "It's still not going the way I want it to go right now, but I'm feeling good, I feel I'm getting stronger, making my pitches, throwing more strikes, getting ahead of more hitters."
Jaso's two-run single in the eighth ended reliever Frank Francisco's string of 12 consecutive scoreless appearances. Jaso added the RBI double in the ninth.
Texas was within 5-4 when Josh Hamilton had a pinch-hit RBI single in the sixth, two batters and the second pitcher after Justin Smoak's RBI single chased Garza. Hamilton was not in the starting lineup after having a cortisone injection in his sore right knee Saturday.
David Murphy's grounder in the fourth drove home a run to get Texas within 3-2, but Vladimir Guerrero was thrown out trying to score on Smoak's grounder to first.