Boston trailed by four runs after three innings, but scored three times in both the fourth and fifth to bring about a 7-7 tie.
The Red Sox then came up with 6 2/3 scoreless innings from their bull pen until the offense finally produced a run that gave Boston its third straight win.
Ryan Lavarnway drew a leadoff walk in the 10th off Tom Wilhelmsen (0-3) and Jackie Bradley came on as a pinch-runner.
Brock Holt sacrificed Bradley to second and, one out later, Jacoby Ellsbury was intentionally walked. That brought up Nava, whose single to center delivered the winning run.
Koji Uehara retired the side in order in the bottom of the 10th, striking out the last two batters for his seventh save.
The win went to Steven Wright (1-0), who made his second major league appearance and won for the first time in his career. He worked 5 2/3 innings in relief of Ryan Dempster, who allowed seven runs in just 3 1/3 innings.