The Aggies (2-1), who went 0-12 in 2005 and carried a 13-game losing streak into this season, have beaten two I-AA opponents so far this fall. New Mexico State opened with a victory over Southeastern Louisiana two weeks ago.
Williams became the first Aggie to score four touchdowns in a game since Chris Barnes did it against New Mexico Highlands in 1999.
New Mexico State's Chase Holbrook was 27-of-42 for 347 yards with one interception, his third straight contest with at least 300 yards passing.
The Tigers (2-1) were led by reserve quarterback Cornelius Harmon, who started for the injured Tino Edgecombe. Harmon threw for 105 yards, completing 10-for-21 attempts with one TD pass.
Texas Southern was within a touchdown through most of the first half but a costly penalty helped New Mexico State pull away.
The Aggies led 14-7 just before halftime and lined up to punt after their drive stalled near midfield. But the Tigers were penalized for being offside, giving New Mexico State fourth-and-1 at Texas Southern's 49.
Holbrook's 1-yard gain kept the driving going, and three plays later Williams streaked down the left sideline for a 35-yard TD run and a 21-7 halftime lead.