GREENSBORO, N.C. — Gerald Henderson finally will find out what the second weekend of the NCAA tournament is like.

Henderson scored 24 points and hit three free throws in the final minute to help Duke beat Texas 74-69 on Saturday night in the second round of the East Regional.

Kyle Singler added 17 points and Jon Scheyer added 13 for the second-seeded Blue Devils (30-6). They reached the round of 16 for the first time since 2006 and will face third-seeded Villanova (28-7) on Thursday night in Boston.

A.J. Abrams scored 17 points on 5-for-13 shooting for the No. 7 seed Longhorns (23-12), who rallied from a late 10-point deficit to tie it twice in the final 2 minutes — the last time coming when Gary Johnson's free throw with 1:07 remaining made it 69-all.

Nolan Smith hit two free throws with 47 seconds left to put Duke up 71-69, and the Longhorns missed two chances in the final 40 seconds to tie it.

Damion James' 3-pointer over Henderson circled the rim and popped out. After Henderson added a free throw with 30.8 seconds left, Abrams missed a runner and James couldn't convert the follow-up.

As the rebound squirted toward the Texas bench, Scheyer made a heady play to chase it down and hurl it downcourt to Elliot Williams. When the freshman missed two free throws with 11.5 seconds left, the rebound bounced off a Longhorn's hands to Henderson, who pumped his fist as he hit the floor, then hit two foul shots with 7.2 seconds remaining to seal it.

Smith finished with 11 points for the Blue Devils, who shot 43 percent. They overcame the Longhorns' 50 percent shooting performance by forcing 15 turnovers and improved to 12-0 in NCAA tournament games at the Greensboro Coliseum — where their two most recent national title runs have started.

A pair of highlight-reel drives to the basket by Henderson helped the Blue Devils build their big lead.

The Duke swingman accelerated down the left wing, leaped and dunked over Clint Chapman as he was being fouled. Two possessions later, he finger-rolled a pretty layup over Abrams to a stretch in which Duke outscored Texas 20-11.

Duke led 64-54 with 7 minutes remaining before Abrams and Varez Ward willed the Longhorns back into the game by keying a 13-3 run. Abrams reeled off five straight points, and Ward finished the spurt with eight in a row for Texas, tying it at 67-all by hitting a jumper over Williams with 1:44 remaining.

Ward, a freshman, scored a season-high 16 points in his second double-figure game of the year and James finished with 15 points for Texas, which has been beaten in the second round twice in three years.

The Longhorns became the second Big 12 team eliminated from the tournament. The conference finished the first round 6-0.

Meanwhile, Duke — one of only two ACC teams still playing — is headed back to some familiar territory.

Reaching the round of 16 never used to be a reason to celebrate after the Blue Devils made it at least that far every year from 1998-2006. But after they followed their first-round exit in 2007 with an equally surprising second-round loss last year, reaching the tournament's second weekend seemed to become a higher priority.

The weekend was a homecoming of sorts for Texas coach Rick Barnes, who grew up a 90-minute drive away in Hickory, once interviewed for a job on Duke coach Mike Krzyzewski's staff and spent four seasons at Clemson. His first victory against the Blue Devils came in 1995 — the last game Krzyzewski coached before he took a leave of absence for the remainder of that season to have back surgery.

This time, after Duke improved to 4-0 against Texas, it was Coach K who was the one sending Barnes into some extended time off — he's got the entire offseason to dwell on this defeat.