The Blue Jays' offense was paced by a rare two-triple night from Alex Rios, who also drove in two runs.
Reed Johnson added a two-run double in support of Chacin (4-1), who allowed seven hits and struck out three.
Scott Kazmir (0-2) suffered the loss, giving up four runs in six innings. It was Tampa Bay's third straight setback.
Rios tripled and scored in the second and then tripled in a run in the fifth to make it 4-1.
Millions of Getty images now available for free via embed tool
NBC reportedly holds celebs hostage to Jimmy Fallon's show