Sheets (3-0) turned in his third win in three starts since joining the Braves after a two-year layoff due to elbow ligament replacement surgery. The right-hander yielded one run on six hits, issuing one walk while striking out four and tossing 58 of his 94 pitches for strikes.
The Braves were leading 2-0 in the fifth when Jason Heyward walked, Chipper Jones hit a ground-rule double and McCann followed with a blast into the right field stands -- the sixth straight game in which he's homered against the Phillies.
Atlanta, which came into the contest holding the second National League wild-card spot, won for the sixth time in eight games.
Philadelphia's Cole Hamels (11-5) walked six batters, surrendering five runs (three earned) on four hits over five frames.
Shane Victorino went 2-for-4 with an RBI double for the Phils.