Lynn (10-4) allowed just one runner to reach third base. The right-hander held Tampa Bay without a hit from two outs in the second until Willy Adames opened the eighth with a double.
Jose Leclerc completed a three-hitter for the Rangers, who moved into a tie for the first AL wild card with the Rays at 46-36.
Tampa Bay was coming off a 3-7 road trip.
Chirinos gave up four runs, five hits and four walks in six innings.
The third inning included a couple wild baserunning plays – one runner was thrown out on a walk, and another scored on an errant pickoff attempt following an infield hit.
Elvis Andrus was on first when Nomar Mazara drew a base on balls. Andrus safely reached second but took off for third when catcher Mike Zunino made an off-target throw to shortstop Adames, who started a rundown that resulted in an out.
Mazara advanced to second on Joey Gallo‘s infield single. The ball was returned to Chirinos, who then made a bad throw to second as an outfielder sneaked in behind Mazara, who scored to make it 4-0.
Odor left in the ninth after it appeared he hurt a leg on a single.
Rangers: AL All-Star DH Hunter Pence (strained right groin) was encouraged after running the bases and could be back next week. … LHP Jeffrey Springs (left biceps tendinitis) has been shutdown. “It didn’t seem to get better with treatment, so that’s when the doctors said ‘OK, there’s something going on in there,’” manager Chris Woodward said.
Rays: CF Kevin Kiermaier, who left Thursday’s game with right calf tightness, didn’t rule out starting Saturday.
Rangers 3B Asdrúbal Cabrera went 0 for 3 with a walk in his return after serving a three-game suspension for hitting an umpire with equipment. Cabrera is hitless in his last 19 at-bats.
JUST MISSED IT
Odor was thrown out at the plate trying for an inside-the-park homer after his sixth-inning hit got past a diving left fielder Tommy Pham. After Pham ran down the ball, he threw it to third baseman Joey Wendle, who made an accurate throw home.
Rays two-way prospect Brendan McKay will make his major league debut Saturday against Rangers RHP Adrian Sampson (6-4). McKay was 3-0 with a 1.08 ERA in five games with Triple-A Durham, where he also got at-bats as the DH.