The catch moved Weineke into a tie with JaRon Harris for third place on the school's all-time list with 24 touchdown receptions.
Lujan finished with 208 yards passing with two touchdowns, Brady Mengarelli had 142 rushing and one score, and Jay Carlson kicked four field goals for the Jackrabbits (6-2, 3-2 Missouri Valley Conference).
In addition to the shutout, the South Dakota State defense held Missouri State (1-7, 0-5) to just 211 yards of offense and 12 first downs.
The Jackrabbits led 22-0 at the break, helped largely by three of Carlson's four field goals.
Ryan Heaston had 73 yards rushing to lead Missouri State, which has lost six straight games.