Villanova (8-1) had pulled to 41-38 with 10:54 to play on a layup by Dante Cunningham, who led the Wildcats with 23 points and 12 rebounds.
Abrams hit a 3-pointer on an inbounds play to make it 44-38 and he capped the 16-9 run by he and James with a 3-pointer with 5:27 left that made it 57-47 and Villanova was never closer than seven points the rest of the way. James also hit a 3 in the run.
The win was the second straight over a ranked team for Texas, which beat then-No. 12 UCLA 68-64 last week.
The game was the first out of the Philadelphia area for the Wildcats, who had won all their games by at least 13 points.
No. 23 Davidson beat West Virginia 68-63 in the opening game of the doubleheader at Madison Square Garden.
Abrams was coming off a career-high 31 points against UCLA and James had 13 points and 13 rebounds in that game.
Both teams came into the game allowing less than 57 points per game and they both kept up their solid defense. Texas shot 41.7 percent for the game (25-of-60), while the Wildcats shot 38 percent (19-for-50), including 4-of-18 from 3-point range, and committed 19 turnovers, six more than the Longhorns.