After the Panthers rallied to within four points late, Pittsburgh forward Shamiel Stevenson was ejected for a flagrant foul with 40 seconds left. Tom Lacy converted both free throws to seal the win.
The Panthers' Ryan Luther hit a 3-pointer with 1:55 left to cut the Navy lead to 66-62.
Shawn Anderson answered with two free throws and Dulin hit one to push Navy's lead back to seven.
The Midshipmen (1-0) opened the second half with a 17-3 run to go up 56-41 as Pittsburgh (0-1) didn't make a field goal for the first 10:46 after halftime.
The Panthers missed 14 of their first 15 second-half field-goal attempts.
But the Panthers responded, scoring 10 straight points to climb back into it. Khameron Davis scored six straight points during the Pittsburgh run.
Anderson had 18 points and eight rebounds for the Midshipmen, who outrebounded Pittsburgh 33-23.
Jared Wilson-Frame led the new-look Panthers with 20 points.
Pittsburgh has 10 new players -- including seven freshmen and two others with no Division I experience -- this season.
The teams traded streaks early on. After the Panthers scored the game's first six points, Navy went on a 17-3 run to take an eight-point lead.
Pitt responded with an 11-2 run of its own to regain the lead 20-19 midway through the first half.
Navy made 19 baskets on 14 assists in the first half and led 39-38 at the break.
The Panthers host Montana on Monday in their home opener. Navy plays at Miami on Sunday.