The Bearkats posted a time of 3:07.10 in the event.
Trey Jones, Brian Hellaire, Jesse Martinez and D. J. Hayes earned their spot in the NCAA semifinals with a school record performance of 3:06.51 in the NCAA West Preliminary Meet in Austin.
The Bearkats finished ahead of Huoston, Texas Southern, Notre Dame and Texas Tech in Thursday night's race.
Penn State produced the best time of the eight qualifying teams which moved into the finals with a mark of 3:01.52.
Other teams moving into the finals were LSU, Mississippi State, Texas A&M, Florida, George Mason, Arkansas and Southern California.
Sam Houston's performance Thursday night marked the second fastest men's 4x400 relay mark in school history. Jones, Hellaire, Martinez and Hayes are the first Bearkat men's 4x400 team to reach the NCAA Division I championship meet.
Charles White of Sam Houston will complete action for the Bearkats Friday competing in the triple jump.