The win keeps alive the chance for an NCAA at-large bid for Villanova (17-10, 8-6 Big East), which has won four of its last five. The Wildcats overcame a poor first half and a 12-point second-half deficit.
Myles Mack had a game-high 24 points for Rutgers (13-12, 4-10), which has lost eight of its last nine games.
Rutgers played without leading scorer Eli Carter, who fractured his right fibula in Saturday's loss at DePaul. Carter, who averaged 14.9 points per game, will miss the rest of the season.
Mouphtaou Yarou had 12 rebounds and 10 points for Villanova, which had five players score in double figures. James Bell added 11 points.
Rutgers matched its biggest lead of the game on Mack's jumper early in the second half that made it 33-21. But Villanova tallied 23 of the next 33 points to go ahead 44-43 with 11:22 left.
Rutgers reclaimed the lead on Austin Johnson's follow that made it 45-44 with 11:05 remaining, but Bell hit a pair of 3-pointers, sandwiched around a layup by Mack, to put the Wildcats back up, 50-47.
Villanova never relinquished the lead again.
The Scarlet Knights hung close, getting within one point on three occasions, but Villanova slowly pulled away. Bell gave the Wildcats some breathing room with 2:45 to play when his 3-pointer put Villanova ahead 65-58.
Nothing came easy in the first half for Villanova.
Villanova led 14-8 after Hilliard's jumper with 12:23 left until halftime, but the Wildcats went ice cold from the floor from that point. They went without a field goal for the next 10:18 until a layup by Pinkston with 2:05 remaining.
Rutgers took advantage, outscoring the Wildcats 23-7 from the 12:23 mark to take a 31-21 lead at the half.
Mack, who scored 12 straight Scarlet Knights points in one stretch, had 16 points at the break.
The Wildcats finished the half shooting 30 percent (6 of 20), including 2 of 10 behind the arc and 7 of 14 from the free-throw line.
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