The Pirates put together a two-out rally to post their second 1-0 extra-inning win of the series. After Neil Walker kept the inning alive with a single, Jose Tabata reached when Freddy Galvis airmailed his rushed throw into the seats.
Harrison dribbled a bouncer through the middle against Jonathan Papelbon (1-1) to bring in Walker and seal the club's fourth straight win.
Burnett had plenty of help from his defense along the way.
Andrew McCutchen stole a hit away from Ryan Howard with a leaping grab at the wall in the first inning, Sean Rodriguez laid out and made a sensational diving grab at the warning track to end the fifth, and Jung-Ho Kang picked a sure Jeff Francoeur hit with his backhand for the first out in the seventh.
The Phillies, losers in nine of 10 overall, put a runner in scoring position in the ninth with one out, but Ben Revere over-slid third base attempting a steal and was tagged out.
Cole Hamels was given no run support as his seven innings of scoreless work went for naught. The left-hander struck out 12 and allowed just four hits and one walk.