Durham (27-30) is 4-2 on a 10-game road trip.
Munson's homer, his ninth, was his second in as many days off Ottawa closer Tim Byrdak (2-1).
It came two batters after a leadoff single by Earl Snyder.
Munson now has hit five of his nine homers off lefties.
Ottawa had taken the lead in the sixth on Ed Rogers' two-out two-run homer.
The Munson homer made a winner out of Durham's third pitcher Franklin Nunez (2-0).
Nunez retired all six batters he faced, and now has retired all 13 batters he's been up against since joining Durham on May 30th.
Jonny Gomes went 3-for-4 with two RBI, a homer, and two runs scored.
Durham meets Ottawa on Sunday at 1:05 p.m., with coverage on WDNC 620 AM beginning at 12:30 p.m.
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