Four relievers followed Cobb, producing all zeros on the scoreboard. Closer Alex Colome got the final three outs to complete the team's sixth shutout of the season while earning his 38th save and clinching the three-game series with the Blue Jays.
The Rays (63-66) and Blue Jays (60-67) continue to try and remain in the hunt in the American League Wild Card race. They began the day with six teams ahead of them for the second Wild Card spot.
Daniel Robertson's sacrifice fly in the second off Tom Koehler scored Corey Dickerson to give the Rays a 1-0 lead.