Derrick Zimmerman drained a 3-pointer as the clock expired that would have sent the Bulldogs to the semifinals in New York, but the shot left his hands just after the buzzer sounded.
Mississippi State coach Rick Stansbury immediately ran to the referees after Zimmerman's shot was waved off and requested they check a courtside replay. The replay confirmed the call on the floor and the Golden Hurricane (24-11) celebrated.
Antonio Reed led Tulsa with 17 points and Kevin Johnson 16. The Golden Hurricane were 10-for-20 from 3-point range.
Mississippi State tied it with 21 seconds left on a layup by Mario Austin, who finished with 12.
Tulsa used some quick passing on its last possession to get Harrington free on the baseline.
Marckell Patterson led the Bulldogs (18-13) with 20 points and Zimmerman had 14, including 11 in the second half.
Tulsa advanced to the NIT semifinals at Madison Square Garden for the second time.
Both teams played road games Monday _ Tulsa in Minnesota and Mississippi in Pittsburgh _ but the quick turnaround didn't seem to have an affect on the play, as both sides kept the pace brisk throughout.
Tulsa held Mississippi State without a field goal for an 8-minute stretch of the first half and were up by 18 with 4:46 left in the first half. Reed, who averages 7.4 points, had 12 in the first half for the Golden Hurricane.
But Mississippi State closed the half with a 14-3 run, highlighted by Zimmerman's crowd-pleasing dunk over two Tulsa defenders, and cut the Golden Hurricane's lead to 38-31 at half.