Tracy Abrams added 14 points for Illinois (10-0) and new coach John Groce is off to the best debut for an Illinois coach in the team's modern history.
Kelly Olynyk scored 16 points to lead Gonzaga (9-1).
Myke Henry's basket gave Illinois its first lead of the game at 44-43 in the opening seconds of the second half, and the Illini pushed that to 54-49 by making all five of their field goals to open the half.
Henry's 3-pointer gave Illinois a 59-51 lead. Two baskets by Przemek Karnowski cut Illinois' lead to 61-58.
But shooting woes hurt Gonzaga in the second half, and D.J. Richardson's 3-pointer gave the Illini a 68-59 lead.
Gonzaga was held without a field goal for 6 minutes, then got consecutive baskets from Olynyk and Gary Bell Jr. to close within 68-64.
Paul replied with two baskets for a 73-64 Illini lead with 5:45 left.
Gonzaga rallied, and Kevin Pangos' free throw cut Illinois' lead to 75-71 with 2:51 left.
But Paul completed a 3-point play to give Illinois a 78-71 lead with 2:29 left. Tracy Abrams hit two more free throws for an 80-71 Illini lead, and Gonzaga started taking desperation shots.
In the first half, Gonzaga made six of its first seven shots to jump to a 14-6 lead. Paul's free throw cut Gonzaga's lead to 20-16, but David Stockton replied with a 3-pointer for the Bulldogs, and they went on to build a 31-20 lead. Illinois fought back with a 12-2 run, and Paul's free throws tied the score at 35.
The score was tied at 41 at halftime, and Paul led all players with 18 points in the half for the Illini.
Illinois, which leads the NCAA with an average of 10.8 3-pointers per game, made 11 of 26 from long range.
Illinois had lost five straight games to ranked teams. Illinois' previous road win over a ranked team came in 2010.