Three of the touchdown passes came in the first half, two to Darrell James, who had six catches for 119 yards. James' 37-yard score with 57 seconds left in the half made it 28-10.
Straub, who was 13 of 29 for 206 yards, connected with Jacob Varble for a 6-yard score late in the third quarter to make it 35-10. The Southern Illinois defense forced four turnovers with Ryan Neal picking off a Jesse Hosket pass and recovering a fumble.
The Salukis (2-0) have won 10 of the last 12 meetings with the Redhawks (0-3) but trail the series 40-37-8.
Hosket was 20 of 38 for 166 yards and a touchdown but was picked off twice and sacked three times.