Loney lined an opposite-field drive off Neal Cotts (0-1) that went over left fielder Shin-Soo Choo and put the Rays up 5-4. Brandon Gomes (1-0) pitched a perfect eighth before Grant Balfour got the final three outs for his first save.
Texas right-hander Nick Martinez allowed three runs and four hits over six innings in his major league debut.
Alex Rios put the Rangers up 2-0 with a two-out, two-run double in the first off Price. Rios has 12 hits in 30 at-bats with 10 RBIs against the Rays left-hander.
Elvis Andrus made it 3-0 on a second-inning RBI single before Escobar pulled Tampa Bay within two on a solo homer in third.
It was announced before the game that Escobar and the Rays had agreed to a two-year extension for 2015 and 2016 worth a guaranteed $13 million. There is a 2017 club option.
After Choo had a sacrifice fly in the fourth, Joyce cut the Rays deficit to 4-3 with a two-run homer in the bottom half.
Rays manager Joe Maddon had a successful challenge for the second straight game. It was first ruled that Robinson Chirinos had beat Escobar's throw from shortstop to first for an infield single in the second, but after a 1-minute, 35-second delay the umpires changed the call to an out.
Maddon won his first replay reversal in the seventh Friday night after it was first ruled that right fielder Wil Myers didn't make the catch while sliding forward on J.P. Arencibia's two-out flare. After a 1-minute, 43-second delay, the umpires ruled Myers did make the catch.
Notes: Rangers ace Yu Darvish (neck stiffness) could throw up to 100 pitches in his first start this season Sunday. ... Alex Cobb (0-1) will pitch Sunday for the Rays. ... Texas 2B Jurickson Profar (right shoulder muscle tear) is fielding grounders, but no date has been set to swing a bat. ... Rangers LHP Joe Saunders (bruised left ankle) played catch and will have his status determined by Monday. ... Martinez had his contract purchased from Double-A Frisco. ... Texas RHP Daniel McCutchen was optioned to Frisco