North Dakota State (8-2, 6-1 Missouri Valley Football Conference), ranked fourth in the FCS coaches poll, heads into its season finale next Saturday against rival North Dakota riding a three-game win streak.
Miller's 5-yard touchdown run capped a 10-play, 69-yard drive early in the fourth quarter. Williams ended a 14-play, 75-yard drive with a 3-yard scoring run with 4:40 remaining to stretch the Bison's lead to 21-10.
Miller completed 6 of 11 passes that included a 27-yard touchdown pass to Kobe Johnson for the Bison in the first quarter.
Nic Baker threw a 6-yard touchdown pass to D'Ante' Cox with 39 seconds left for Southern Illinois (5-5, 4-3), which has lost three straight. Baker was 14-of-23 passing for 174 yards and also threw an interception.
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