With the Cornhuskers clinging to a 60-59 lead with 2:40 to play, Watson hit jumpers on back-to-back possessions. Evan Taylor made a pair of free throws in the final minute, and Nebraska survived for an opening win.
Senior guard Terrell Lewis scored 13 points and Jajuan Starks added 12 for the Panthers (0-1), who beat Illinois in an exhibition game in the preseason. Eastern Illinois and had its sights on knocking off another Big Ten opponent Saturday.
The game was close throughout. Montell Goodwin hit a 3-pointer that gave Eastern Illinois its largest lead at 54-48 with 9:14 left in the second half.
Nebraska would not go away and regained the lead on a pair of free throws by James Palmer Jr. with five minutes to play. Palmer and Taylor each finished with 12 points for the Cornhuskers (1-0).
It was a back-and-forth, tight first half, with neither team leading by more than five points. Nebraska guard Thomas Allen hit a 3-pointer that tied the score 27-27 with four minutes left in the first half.
Palmer had a fast-break dunk and knocked down a jumper in the final two minutes of the half to help the Cornhuskers take a 34-33 lead into halftime. Palmer had 10 points to lead all scorers in the first half.