The Cougars (5-4) recovered from last week's three-point loss at No. 5 Notre Dame by holding Georgia Tech's triple-option attack without a rushing touchdown for the first time in two years and without an offensive touchdown for the first time since 2008.
"I was just so glad to see them get a victory," said BYU head coach Bronco Mendenhall. "We have had three losses by a total of seven points against good teams. I'm just proud of how hard they've been working."
"I might not be so big," said Williams, who accounted for 161 total yards. "But I think it's just my heart and determination to have my team succeed. I just tried to come out aggressive and not be easy to take down. I feel like I did a great job of that today."
Georgia Tech (3-5) has lost three of four. The Yellow Jackets' offense failed on all 10 of its third-down attempts while their defense was gouged for 411 yards.
BYU, which began the afternoon with the nation's fourth-ranked defense, did not allow an offensive touchdown for the fifth time this season.
The Cougars never trailed after opening with a 17-play, 75-yard drive that ended with Williams converting a fourth-and-goal from the 6.
Georgia Tech tied the game at seven on an interception return by Isaiah Johnson. It was Nelson's third interception return for a touchdown this season.
But after a 1-yard touchdown run by Williams, Kyle Van Noy blocked a punt setting up a Nelson up a 10-yard touchdown run to make it 21-7 BYU.
For the day, Nelson finished 19 of 28 for 204 yards, one touchdown run and one touchdown pass. The Cougars out-gained the Yellow Jackets 411-157 and dominated time of possession 38:59 to 21:01.
"I think we were able to establish the run," said Nelson, who threw a shovel pass to Williams for a 39-yard touchdown. "A lot of credit goes to our five guys up front. Jamaal Williams did a real great job of patient, smart running. That helped open it up for us to get some shots downfield."
BYU next hosts Idaho November 3rd.