During the course of the contest, B.J. Upton and Gabe Gross had an outfield collision allowing a ball to fall in; shortstop Jason Bartlett and left fielder Carl Crawford got confused, prompting Crawford to back off, then Bartlett couldn't make the catch; starter Matt Garza went off on catcher Dioner Navarro; and Eric Hinske got ejected for arguing balls and strikes.
Despite Sunday's loss, the Rays claimed their 11th series win in their last 14 series, but they fell to 1 1/2 games behind the American League East-leading Red Sox, who defeated the Mariners, 2-1.
"This wasn't a pretty day today," Crawford said. "Bad day all around, but we still won the series. And that's one of our goals, you can't sweep them all. Give them credit, they played well today."
Rays manager Joe Maddon did not have a problem with his team's effort, though he said they came out a little flat initially.
The Rangers "showed us some offense today, but they didn't just blow it up on us," Maddon said. "We kept it tight. ... We had opportunities, good at-bats, but it wasn't our day from a directional perspective. We just couldn't find the holes."
David Murphy homered in the first inning off Garza to put the Rangers up, 1-0. German Duran added a two-run homer off Garza in the fourth to push the lead to 3-0.
Jason Hammel took over for Garza in the fifth after Garza and Navarro exchanged words on the mound and the spat spilled over to the Rays' dugout. Hammel walked two of the first three hitters he faced before Gerald Laird singled home the Rangers' fourth run.
Upton hit a two-run homer in the sixth off Rangers starter Doug Mathis to cut the lead to 4-2 and the Rays had a chance to tie it up in the seventh when Akinori Iwamura hit with two outs and runners on second and third, but he was called out on strikes by home-plate umpire James Hoye.
Afterward, more than one member of the team expressed displeasure with Sunday's strike zone. Hinske voiced his displeasure during the game.
"I thought [the pitch] was a ball, I let him know I thought it was a ball, I thought it was outside," said Hinske, who expressed the expletive he said to Hoye. "I thought it was a pretty quick trigger. I've said a lot worse to umpires in my career and haven't gotten thrown out. So be it.
"I apologized to Joe [Maddon] for leaving him shorthanded there. But I didn't think I did anything to get thrown out of the game. But it was kind of an ugly day all around. Hopefully we can just put this game behind us and go into Anaheim and get some wins."
As ugly as the players thought the game was, they seemed to have already turned the page.
"The bottom line is you try to win series all the time and we won two out of three here," Hinske said. "We've got to take positives from it. Winning series is our goal all the time, two out of three, three out of four, and we did that here."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.