Holman had 16 points and 10 rebounds and Ado had 15 points and nine rebounds as the fourth-seeded Bulldogs (23-11) advanced to meet No. 1 seed Baylor on Sunday.
Xavian Stapleton had 12 points and Lamar Peters didn't score but contributed 14 assists in the Bulldogs' first postseason victory since an 81-67 triumph against Jackson State in the 2010 NIT.
The Bulldogs played without SEC All-Freshman guard Nick Weatherspoon, who suffered a hip contusion during a fall in the Bulldogs' 62-59 loss to Tennessee in the quarterfinals of the SEC tournament last week.
James Palmer Jr. scored 13 points, Isaac Copeland Jr. had 12 and Isaiah Roby 10 to lead fifth-seeded Nebraska (22-11).
MSU led by five points at halftime, but Nebraska made three 3-pointers and converted a three-point play to pull even at 40.
Holman scored the next five points and the Bulldogs maintained that margin as they took a 50-45 lead after three quarters.
Copeland Jr. and Jordy Tshimanga each made a basket and Palmer hit two free throws to give the Huskers a 51-50 lead with 7:41 remaining.
Stapleton's layup gave the lead back to the Bulldogs and Tyson Carter scored four points as they took a 58-53 lead with 2:18 left.
Quinndary Weatherspoon's 3-pointer pushed the lead to 61-53 with 1:46 left as Nebraska made just one field goal in a seven-minute span.
Roby and Anton Gill made consecutive baskets to get the Cornhuskers within 61-57, but Stapleton made two free throws with 41 seconds left.
Ado scored the final six points for MSU as it finished on a 10-4 run to take a 19-12 lead after one quarter.
The Huskers scored the first seven points of the second quarter to pull even before Holman ended the streak with a 3-pointer.
Nebraska got within one point before Ado converted a three-point play and Stapleton made a 3-pointer to give the Bulldogs a 30-23 lead.
The Huskers scored the next five points before Carter's 3-pointer gave MSU a 33-28 halftime lead.
--Field Level Media
Nebraska | Mississippi State | |
James Palmer Jr. 13 | Scoring | Aric Holman 16 |
James Palmer Jr. 5 | Assists | Lamar Peters 14 |
Isaiah Roby 8 | Rebounds | Aric Holman 10 |
James Palmer Jr. 3 | Free Throws Made | Abdul Ado 3 |
Glynn Watson Jr. 3 | Steals | Tyson Carter 1 |
James Palmer Jr. 2 | Blocks | Aric Holman 4 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Nebraska | 59 | 35.4 | 6-22 | 7-9 | 10 | 27 | 4 | 6 | 5 |
Mississippi State | 66 | 42.1 | 6-18 | 12-18 | 16 | 43 | 7 | 2 | 13 |