Glennon and UConn quarterback Chandler Whitmer each threw for 204 yards. But Whitmer also had three passes intercepted as the Wolfpack (1-1) forced four Huskies turnovers.
All-America cornerback David Amerson, burned deep twice in NC State's season-opening loss to Tennessee, recorded his 14th career interception and knocked away a fourth-down pass on Connecticut's final drive to secure the win.
Glennon completed 15 of his 30 passes but was sacked six times. NC State had just 258 yards of offense but held the Huskies (1-1) to 239.
UConn's Lyle McCombs rushed for 60 yards and caught a 43-yard swing pass that set up his 5-yard fourth-quarter touchdown run to pull UConn to within three points with 7 minutes left.
Glennon opened the next drive by hitting Tobais Palmer with two quick passes to move into UConn territory. But the Huskies defense stiffened at the 27, and the Wolfpack, heading into a stiff wind, decided to go for it on fourth-and-2. Glennon's pass to Underwood fell incomplete, giving UConn one more drive with 3:17 remaining.
Whitmer moved the Huskies from their own 27 to the 46 before being sacked by linebacker Brian Slay on third down and having Amerson knock down the fourth-down pass.
A bizarre UConn turnover led to NC State's touchdown. Safety Earl Wolff tipped a Whitmer pass into the hands of Huskies tight end John Delahunt, who then fumbled the ball back to Wolff. Three plays later, Underwood ran under a Glennon pass, catching it with his fingertips at the 18-yard line and running the rest of the way into the end zone for a 10-0 lead.
Amerson picked off Whitmer's pass on the next UConn play, but Niklas Sade's 44-yard field-goal attempt went wide right.
The first points didn't come until late in the second quarter, when NC State put together the game's first sustained drive of 15 plays.
But after moving 61 yards, a sack by Trevardo Williams forced the Wolfpack to settle for a 40-yard field goal from Sade with just under 3 minutes left in the first half.
Connecticut's best scoring chance before halftime came when Nick Williams' 30-yard catch set the Huskies up at the NC State 37. But after a penalty, Whitmer tripped and fell while dropping back, and an 18-yard catch by Williams set up a fourth-and-2. UConn went for it rather than try a 47-yard field goal into a stiff wind, and Whitmer was sacked by linebacker Rickey Dowdy.
UConn won the early battle for field possession but could not capitalize. The Huskies failed to get a first down after starting their first three drives on their own 39, 48 and the NC State 45. The Huskies didn't have a first down until the end of the quarter when NC State's T.Y. McGill was called for roughing Whitmer.
The Huskies had just 111 yards and four first downs at halftime, but their defense held NC State to 116 yards in the half. Of the 69 plays before intermission, only 38 of them went for positive yards.
NC State is now 9-1 in games following a loss since the start of the 2010 season.
UConn, which plays Maryland next week, falls to 4-11 in games against the Atlantic Coast Conference.
Wolfpack coach Tom O'Brien improved to 5-4 against teams from the Big East, including wins in four of the last five matchups.
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