Already leading 4-1, the Yankees blew the contest open with the big frame.
Then, after Curtis Granderson and Nick Swisher each drew bases-on-balls, Cano drilled a 1-2 pitch into the right-field stands for his ninth career grand slam.
Jeter finished 3-for-4 with three RBI and Granderson added a solo shot -- his 29th of the year -- as the American League East-leading Yankees avoided a three-game sweep.
Phil Hughes (11-8) earned the victory, allowing one run on nine hits over six innings.
Britton was tagged for seven runs on seven hits in his 2 2/3-inning stint.
J.J. Hardy went 3-for-4 with a solo homer for Baltimore.