Texas scored the game's first eight points and led by as many as 19 in the first half.
North Carolina fought back, however, and trailed only 60-56 when Reggie Bullock hit a jumper with 7:50 to play.
The Longhorns then ran off five quick points to create some breathing room with Lewis hitting a jump shot that put Texas in front 65-56. The Tar Heels came no closer than seven the rest of the way.
Sheldon McClellan led Texas (7-4) with 18 points, Lewis had 16 and Jonathan Holmes contributed 15 points and eight rebounds.
Bullock had 18 for the Tar Heels (8-3). North Carolina had won three in a row.