"It's big ... just to come out here and beat this team," Myers said.
Tampa Bay and Texas started play one-half game ahead of Cleveland, which was at Kansas City, in the race for the two wild-card spots.
Myers had a second-inning solo shot and hit a two-run double during a four-run fifth. Cobb (9-3) allowed two runs, six hits, one walk and had 10 strikeouts.
"At this point of the season, the position we're in, every game is going to get bigger and bigger," Cobb said. "Yesterday was the biggest game of the season, today is the biggest game of the season, tomorrow will be the biggest game of the season. I don't think it's unfair to say that. We realize the performance we have to put together out there every night, and I think we're up for it."
Matt Garza (9-6) gave up six runs and eight hits over 4 1/3 innings to lose his third straight start for the Rangers, who have lost seven in a row and are 2-12 in September. Garza is 3-5 with Texas since being acquired from the Chicago Cubs on July 22.
Texas has not held a lead during the current skid.
"I'm not frustrated, I'm confused," Rangers manager Ron Washington said. "I'm trying to figure out what we have to do to jump-start this offense."
The announced crowd was just 10,724. The Rays entered with the major's lowest home attendance average of 18,747.
"Those were really big knocks right there," Rays manager Joe Maddon said of Myers.
Garza, who was the MVP of the 2008 AL Championship Series when Tampa Bay beat Boston, pitched against the Rays for the first time since being traded to the Cubs on Jan. 8, 2011.
"My job is to help us get to October and I'm still going to keep trying, keep pushing, keep working and get ready in five days," Garza said. "Keep grinding."
The Rays took a 2-1 lead in the fourth on Desmond Jennings' sacrifice fly.
Myers put the Rays up 1-0 on his 13th homer, an opposite-field drive to right in the second.
Cobb retired nine in a row, including his first four batters on strikeouts, before Kinsler doubled to start the fourth. After advancing to third on a sacrifice bunt by Elvis Andrus, Kinsler got tagged out during a rundown on Alex Rios' grounder to third.
A.J. Pierzynski tied it at 1 later in the fourth with an RBI single.
Myers flew out to the center field fence with the bases loaded to end the sixth. ... The Rangers held a players only meeting before batting practice. ... Rays reliever Jesse Crain (strained right shoulder) threw in a simulated game and will have his status evaluated Tuesday. ... Texas DH Lance Berkman (left hip and right knee) was in the starting lineup for the first time in two weeks and went 0 for 4. ... The Golf Channel's Holly Sonders used a golf club from in front of the mound to hit a ball to the plate for the ceremonial first pitch.