The Wildcats (11-1) will host either McNeese State or New Hampshire in the quarterfinals on Dec. 5. It will be the second consecutive trip to the quarterfinals for Villanova, which lost to James Madison 31-27 last season.
Whitney, who finished with 62 yards rushing, broke a 14-14 tie in the second quarter with a 1-yard touchdown run. The Wildcats kept hold of their lead en route to their sixth straight win. They have also won 17 of their last 18 games at home.
Villanova built a 28-14 lead on Angelo Babbaros 2-yard score with 57 seconds left before halftime.
The Crusaders eventually got within 35-28 with 13:37 remaining in regulation when Alex Schneider caught a 5-yard touchdown pass from quarterback Dominic Randolph.
But the Wildcats responded with a 13-play, 56-yard drive capped by Nick Yakos 25-yard field goal with 7:18 left for a 38-28 advantage.
Matt Szczur had 130 yards receiving on seven receptions for Villanova. Whitney was 16-for-23 passing for 239 yards, including a 29-yard touchdown pass in the opening quarter.
Dominic Randolph, who was 31-for-51 passing, threw for 347 yards and three touchdowns for Holy Cross (9-3), which still has never won an NCAA playoff game.
It was the Crusaders first trip to the postseason since losing to Western Carolina, 28-21, in the quarterfinals on Dec. 3, 1983.