Senior center Isaac Haas contributed 12 points and 10 rebounds for the third-seeded Boilermakers (27-5). Purdue shot 54 percent from the field and was 13 of 30 from 3-point range.
Freshman guard Geo Baker scored 25 points for the 14th-seeded Scarlet Knights (15-19). Junior guard Corey Sanders added 23 points for Rutgers, which shot 47.1 percent from the field.
The Boilermakers face seventh-seeded Penn State (21-12) in Saturday's semifinals.
"Obviously, it starts with Tony Carr," Purdue coach Matt Painter said of the Nittany Lions' star guard in a postgame interview with the Big Ten Network. "... They have a really good team. You know they are going to play hard."
Rutgers was positioned well for a possible upset when trailing by three with Sanders going to the free throw line with 30 seconds left. But Sanders missed the front end of the 1-and-1, and Carsen Edwards and Vincent Edwards each hit two free throws to make it a three-possession game with 15.6 seconds left.
Purdue trailed by three points at halftime but came out strong in the second half with 11 straight points.
Senior guard Dakota Mathias, Carsen Edwards and Vincent Edwards each hit 3-pointers during the charge as the Boilermakers took a 46-38 advantage.
A three-point play by senior guard Mike Williams allowed the Scarlet Knights to trail 56-55 with 11:38 to play. Just more than three minutes later, Baker converted a three-point play to knot the score at 62.
The score was again tied at 64 before Purdue put together a 10-3 run to take a seven-point lead with 4:38 to play.
Rutgers pulled within 78-75 after a basket by Sanders with 1:31 to play.
Baker scored 12 points and Rutgers led for most of the first half while taking a 38-35 lead into the break.
Sophomore forward Issa Thiam and Baker drained consecutive 3-pointers to give the Scarlet Knights an early 13-5 lead. Purdue tallied the next seven points to move within one, but Rutgers responded with six straight and took a 19-12 advantage on Baker's layup with 8:48 remaining.
The Boilermakers later were within 29-28 before Rutgers responded with a 7-2 push, with Baker capping it with a 3-pointer with 1:20 to play.
--Field Level Media
Rutgers | Purdue | |
Geo Baker 25 | Scoring | Carsen Edwards 26 |
Corey Sanders 4 | Assists | Dakota Mathias 7 |
Mike Williams 8 | Rebounds | Isaac Haas 10 |
Geo Baker 1 | Free Throws Made | Carsen Edwards 10 |
Issa Thiam 2 | Steals | Dakota Mathias 2 |
Shaquille Doorson 1 | Blocks | Isaac Haas 2 |