Rashaad Penny, the nation's second-leading rusher coming in, was held to 107 yards on 25 carries for his lowest of the season. He did catch a 33-yard scoring pass from Christian Chapman in the first quarter.
Penny was poked in the eye by Antonio Jones-Davis while at the bottom of a pile in the second quarter and came off the field in pain. He went into the locker room and came back out with a visor installed in his facemask.
SDSU (5-0) is off to its best start since going 8-0 to open the 1975 season. It finished 8-3 that year.
The Aztecs took a 31-14 halftime lead and had to hold on after NIU (2-2) closed to 31-28 in the third quarter. Daniel Santacaterina threw his third TD pass of the night, an 81-yarder to Spencer Tears, on the second play of the quarter, and Marcus Childers scored on a 1-yard run.
John Baron's 21-yard field goal on the second play of the fourth quarter gave SDSU a 34-28 lead.
It took two interceptions in the final minutes to seal it, first by Kameron Kelly deep in SDSU territory and then by Thompson with 1:42 left.
Washington, Penny's backup, got the crowd buzzing with the Aztecs' eighth kickoff return for a score since 2015.
The Huskies had two good drives capped by touchdown passes from Santacaterina to Christian Blake, the first for 34 yards and then for 10 yards.
They were sandwiched around a fumble by Andrew Parchment that was recovered by Andrew Aleki. On the next play from scrimmage, Chapman hit Penny coming out of the backfield for a 33-yard score and a 14-7 lead.
With the score tied at 14, Thompson Ñ who played at San Diego's St. Augustine High Ñ jumped a route and raced into the end zone, with Santacaterina his closest pursuer.
Chapman threw an 8-yard TD pass to Kahale Warring, and Baron kicked a 38-yard field goal for a 31-14 halftime lead.
Jordan Huff had 148 yards on 25 carries for NIU.