The top-seeded Jayhawks built a 19-point lead at intermission and set up a Midwest Region title game against upstart Davidson Sunday.
Kansas ran its record to 34-3 by shooting 51 percent from the field and limiting Villanova to three three-point field goals in 17 attempts.
The Wildcats took an early 6-5 advantage before going on a 21-4 run. Robinson and Rush combined to score 17 points in that surge.
Robinson finished with 15 points and Rush had 14, as did Mario Chalmers.
Kansas held its third opponent in the tournament to less than 40 percent shooting from the field and now will face Stephen Curry, who has scored at least 30 points in each of Davidson's triumphs.
Villanova (22-13), which was seeded 12th in the region, was led by Scottie Reynolds with 11.
With Kansas and Texas both reaching the Elite Eight Friday, the Big 12 is the only conference to have two teams remaining in the tournament. The other six left are from the ACC, Big East, Southern, Conference USA, Pac-10 and Atlantic 10.