Sandoval then hit a pair of free throws before Clifford again hit a deep 3 to make it 54-53 with 15 seconds remaining.
Johnson hit one of two foul shots, giving Holy Cross (6-1) a chance to tie or win, but the Crusaders turned the ball over as time expired.
Jimmy Binnie scored 13 points to lead Dayton, while Clifford had a game-high 20 for the Crusaders.
Dayton led 26-25 at halftime but Clifford and Alex Vander Baan combined to trigger a 13-2 run that gave Holy Cross a 40-33 lead with 10:40 to play.
But Dayton forced eight turnovers in a 15-3 run to take a 48-41 lead with 6:12 remaining.