Jamison had 12 points and 15 rebounds and the Tigers scored 20 second-chance points in defeating Rutgers 78-68 Tuesday night to advance to the quarterfinals of the NIT.
Clemson (18-14) can advance to the semifinals in New York City by beating Butler (22-9) on Thursday night at Littlejohn Coliseum. Rutgers finished 19-13.
``Getting to the NIT final four and Madison Square Garden can erase all the negative thoughts we've had throughout this season,'' Jamison said.
Neither Clemson's men or women have advanced to a final four in either the NCAA or NIT.
``It's exciting for our guys and something to hang our hats on, because like Rutgers, we suffered a disappointing stretch in our season where we dismissed two players and lost six straight,'' first-year coach Larry Shyatt said.
``You're talking about a guy who loves them not because of their basketball, so it makes me feel very good to see some good things happen to them, and I hope it continues to happen for them.''
If Clemson can dominate inside against Butler the way it did against Rutgers, the Tigers have a good chance of winning.
Clemson outrebounded Rutgers 43-29 and got balanced scoring on a night when point guard Terrell McIntyre struggled despite scoring 16 points and handing out nine assists.
Will Solomon added 15 points and Andrius Jurkunas 14 for Clemson, which shot 49 percent from the field.
Dahntay Jones had 20 points to lead Rutgers, which was making its first postseason appearance since 1992. Rob Hodgson added 13 and Jeff Greer 11.
``We got to the second round of the NIT this year,'' Rutgers point guard Geoff Billet said after scoring nine points in his final game. ``Hopefully, this will make them more hungry to go farther next year.''
Clemson never trailed after a 23-9 spurt that bridged the final 6:38 of the first half and the opening 4:33 of the second. Tom Wideman had three put-back baskets during the run in which he scored all eight of his points.
Jurkunas' spectacular one-hand tip capped the run and gave Clemson a 47-33 lead with 15:27 to go.
The lead was still 14 points when Rutgers rallied by hitting five of six shots in a 14-4 spurt. Billet hit a 3-pointer to close the Scarlet Knights to 55-51 with 9:36 to go.
With the lead still four points two minutes later, Clemson put the game away by scoring 10 of the next 12 points, capped by Jamison's slam.
Clemson used its size and defense to fuel two first-half spurts and take a 40-29 lead.
After Rutgers scored the first seven points, the Tigers reeled off 17 in a row while forcing the Scarlet Knights to miss nine straight shots. Jurkunas got the first five for Clemson with a 3-pointer and two free throws.
The Scarlet Knights responded with a 17-7 spurt and tied the game at 24 on a rebound follow by Joel Salvi with 7:02 left in the half.
Clemson didn't allow another basket the rest of the half and took the lead for good on Wideman's first rebound follow.