With two outs in the top of the 10th, Geovany Soto bashed a pitch off the center field wall against Kyle Farnsworth (1-4), with pinch-runner Leonys Martin coming in to run for him.
The next batter, Profar, then scalded a grounder past diving Rays first baseman Carlos Pena and down the right field line, scoring Martin with the go-ahead tally.
Mike Adams (5-3) collected the win and Joe Nathan racked up his 31st save for American League West-leading Texas, which won for the fifth time in seven games and evened its three-game series.
Starter Yu Darvish yielded only two hits through eighth innings, allowing one earned run.
Tampa Bay's Chris Archer, making this third major league start, tamed the Rangers on two runs through seven innings, striking out 11.
Sam Fuld got the only RBI for the AL wild card-contending Rays.
LGBT community has 'bullied the American people': Bachmann
Duggar sisters unveil Christian dating rules in new book