It was the second consecutive season SIU has beaten an FBS school — and the first FCS-over-FBS result this season.
Baker, who also passed for 148 yards, scored on an 8-yard run with 1:58 left in the first quarter to put the Salukis (2-0) up 7-0. Elliot pushed the lead to 14-0 early in the second quarter with a 10-yard scoring run.
Jake Seibert's 27-yard field goal pulled the Huskies (1-1) within 11 points at halftime.
The only scoring in the second half came 47 seconds into the final quarter when Rocky Lombardi connected with Kacper Rutkiewicz for a 62-yard touchdown and then converted the two-point pass to get the Huskies within three points. The TD completed a nine-play, 99-yard drive.
Baker competed 16-of-24 passes for Southern Illinois. Elliott finished with nine carries for 58 yards.
Lombardi completed 21-of-37 passes for 297 yards with two interceptions. Rutkiewicz finished with six catches for 139 yards.
AP college football: https://apnews.com/hub/college-football and https://apnews.com/hub/ap-top-25-college-football-poll