Fernando Perez drove home the go-ahead run with a squeeze bunt in the ninth inning for Tampa Bay, which overcame a five-run deficit to beat Texas 7-6 on Sunday, spoiling the Rangers' home finale and hurting their already slim playoff hopes.
The Rangers led 5-0 when Brandon McCarthy threw his last pitch with two outs in the eighth, after an error by third baseman Chris Davis extended the inning. Four relievers faltered after that.
Ben Zobrist hit a two-run single in the eighth and ninth for Tampa Bay, which avoided its second sweep in Texas this season.
With seven games left, the Rangers trail by six in the division and wild-card race. The Angels beat Oakland 7-4 on Sunday, and wild-card leader Boston lost 4-2 at the New York Yankees.
Perez, who entered as a pinch runner in the eighth, laid down the bunt after Zobrist's two-run single in the ninth off Frank Francisco (2-3). Carl Crawford also had an RBI single in the inning.
McCarthy gave up two runs, both unearned, and six hits over 7 2-3 innings in his fifth start since spending nearly two months on the disabled list because of a stress fracture in his right shoulder blade.
The right-hander quickly got the first two outs in the eighth before the error by Davis and a walk. Darren O'Day and C.J. Wilson both faced two batters and failed to retire any of them, before Francisco came on to strike out pinch-hitter Gregg Zaun.
But Francisco, who had converted 24 of 27 saves, got himself in trouble in the ninth. The right-hander walked two and gave up three hits before hard-throwing rookie Neftali Feliz took over to face Perez.
Randy Choate (1-0), the fourth of six Tampa Bay pitchers, gave up the homer to Byrd in his only inning. Lance Cormier got the final out for second save.
The Rangers went in front on Cruz's 33rd homer, a two-out shot in the second that snapped a 4-for-30 slump.
Cruz also had a leadoff single and scored in Texas' three-run fifth against rookie left-hander David Price. Ian Kinsler doubled in Cruz before Elvis Andrus' squeeze play turned into an run-scoring bunt single and David Murphy hit a sacrifice fly.
The drive by Byrd, who went deep twice in Saturday's 15-3 victory, gave him his first 20-homer season.
After replacing McCarthy in the eighth, O'Day walked Evan Longoria and gave up a two-run single to Zobrist that made it 5-2. Wilson allowed an RBI single to Willy Aybar and hit B.J. Upton with a pitch before Francisco came in.
NOTES: A strange ending to the Rangers fifth: On the same pitch Byrd drew a walk Andrus was caught stealing at third for the third out. Byrd, who hadn't even left the batter's box, still had to go to first base to be credited with the walk.