Stephen F. Austin (3-5, 3-3 Southland Conference) was up 27-14 at the half but Incarnate Word's Kody Edwards returned the second half kickoff 100 yards to close the gap to 27-21. The Lumberjacks then scored 28 unanswered points.
Conque, who completed 22 of 33 passes, also rushed for 35 yards. Loren Easly led all rushers with 85 yards and Aaron Piper pulled in six passes for 139 yards and two scores.
Trent Brittain threw for 208 yards and one touchdown for Incarnate Word (4-4, 3-3). The Cardinals were limited to 73 yards rushing.
The Lumberjacks, who started the season with five straight losses, have now won three consecutive games. They face Central Arkansas on Saturday.