Rowe made 9 of 14 free throws and moved into first place on the school's all-time list with 520 makes in her career.
Middle Tennessee (24-4, 13-1 Conference USA) made just 18 of 45 field goals and 4 of 13 3-pointers but recorded season highs by making 30 of 49 free throw attempts.
East Carolina (21-6, 9-5) converted 8 of 17 (47.1 percent) from the line.
Trailing 34-33 at halftime, the Blue Raiders opened the second half with a 13-2 run as ECU made just 1 of 11 field goals, and committed six turnovers, in the first 10 minutes.
The Pirates never threatened again.
KeKe Stewart added 18 points and Shanice Cason 16 and eight rebounds in the win.
Jada Payne paced ECU with 18 points.