The conversion followed Sasek's 3-yard touchdown pass to Jones to complete a 3-play, 51-yard drive, set up when the Fightin Blue Hens recovered an onside kick.
Delaware (7-2, 4-1 Colonial Athletic Association) cut the lead to seven just 29 seconds earlier when Sasek (34 of 46, 330 yards) found Michael Johnson open for an 11-yard score.
Towson (8-2, 4-2) led 31-10 after a Drew Evangelista 25-yard field goal at 14:31 of the fourth quarter.
Delaware started its comeback with a 56-yard drive, capped by Jalen Randolph's 1-yard touchdown run to cut the score to 31-17.
Towson's Terrance West added to his nation-leading totals in both rushing yardage and touchdowns with 206 yards and 2 TDs -- his third 200-plus yard game this season.