On a night when ACC player of the year Greivis Vasquez was having trouble scoring, Maryland turned to freshman forward Jordan Williams.
Williams led four players in double figures for Maryland (24-8), which advanced to play Sunday against fifth-seeded Michigan State, a 70-67 winner over New Mexico State.
Aubrey Coleman, the nation's leading scorer, had 26 points for 13th-seeded Houston (19-16). The senior averaged 25.6 points per game this season. Kelvin Lewis added 24 for Houston, 17 in the second half.
Maryland overpowered the Cougars 50-29 on the boards and held them to 41 percent shooting. Houston was also hurt by 20-of-32 shooting from the free throw line.
The Terrapins made 21 of 25 free throws, which helped them keep Houston from making a run in the second half.
Landon Milbourne added 19 points, Vasquez 16 and Eric Hayes 11 for Maryland. The 6-foot-10 Williams made nine of 14 shots.
Maryland has been to the NCAA tournament eight times this century. This was Houston's first appearance since 1992.
With Vasquez held to six points, Maryland still led 43-42 early in the second half. Then the Terrapins went on a 12-2 run, capped by Adrian Bowie's 3-pointer, for a 55-44 lead with 16:45 left.
Lewis replied with five straight points for Houston to close the gap to six. But Maryland worked the lead back to double digits, mostly at the free throw line.
After Zamal Nixon's free throw brought Houston within 72-63, Williams' layup pushed the lead back to double figures with 6:49 remaining.
Houston would not go away. Adam Brown's 3-pointer and three free throws by Lewis cut Maryland's lead to 78-69 with 5 minutes left. But that margin held, as Coleman went 11 minutes without scoring late in the second half.
In the first, Houston held a 24-22 lead despite making just eight of its first 25 shots. Coleman had 11 of those points.
Maryland pulled ahead 27-25 on Bowie's 3-pointer. Williams put back a couple of missed shots as Maryland built a 35-29 lead with 2:27 left in the first. Williams had 10 points and 10 rebounds in the first.
Maryland was leading 39-31 with a minute left when Lewis sank a long 3-pointer. After the Terrapins missed, Houston rebounded with a few seconds left and Brown hit a long, running 3 at the buzzer to cut Maryland's lead to 39-37 at halftime.
Coleman had 16 points in the first half.
Houston qualified for the NCAAs by winning four games in the Conference USA tournament and beating top-seeded UTEP in the final. It was the Cougars' longest winning streak of the season.
This was the first time the teams met since the 1983 NCAA tournament during Houston's Phi Slama Jama heyday.
Maryland shared the ACC regular-season title with Duke, but lost to Georgia Tech early in the conference tournament. The Terrapins drew an at-large bid to make their 17th consecutive postseason appearance.
In an odd twist, Maryland coach Gary Williams and Houston coach Tom Penders both entered with 648 career victories, tied for fifth among active coaches.
Penders, in his 36th season, was taking a team to the NCAA tournament for the first time since he coached George Washington in 1999. This was his 11th NCAA appearance