The Rangers celebrated their first American League West title since 1999 with the victory over second-place Oakland.
Cantu finished 3-for-4 with a pair of RBI and Michael Young added a pair of hits and an RBI in the win.
Texas closer Neftali Feliz made the lead hold up with a scoreless ninth, notching his 38th save of the save of the year despite surrendering a one-out double to Jeremy Hermida.
Feliz's save total set a major league record for a rookie, surpassing the Mariners' Kazuhiro Sasaki in 2000.
Darren O'Day (5-2) collected the victory after tossing a scoreless eighth. Rangers starter Derek Holland allowed only one run over five innings of work.
Michael Wurtz (2-3) was tagged with the loss for the A's, who got a two-run homer from Cliff Pennington.