Kansas State (6-3) overcame a poor second-half performance from the foul line to top the Coyotes. While holding a 63-62 lead with 2 seconds left, Thomas Gipson converted on the first of two free throws to seal the victory.
South Dakota opened strong, charging to a 15-4 lead with 10:59 remaining in the first half. Having returned four of its five starters from last season, the Coyotes used their experience to punish a depleted Kansas State frontcourt with 16 points in the paint in the first half.
The Wildcats twice cut the lead to three but South Dakota maintained a five-point advantage at the break.
Foster's 4-for-7 shooting from 3-point range kept Kansas State within breathing range.
But the Coyotes limited the defending Big 12 champions to 32 percent shooting in the first half while also forcing 11 turnovers.
Having seen limited offense before the break, Gipson opened up the second half with two consecutive baskets while Omari Lawrence added two of his nine second-half points.
Neither team was able to stake its claim on the lead as the second half alone carried 17 lead changes and four ties.
A 3-pointer from Southwell gave the Wildcats a 59-57 advantage with 4:52 left. The Wildcats held the lead for the remainder of the contest.
Maintaining its edge on rebounding proved to be crucial for the Wildcats. Four different players grabbed at least five rebounds including Gipson leading the way with eight.
South Dakota attempted to close the gap by putting the Wildcats on the free throw line and it nearly paid off.
The Wildcats closed the game with a 3-8 performance from the line, and a half-court heave from South Dakota's Brandon Bos fell short at the final buzzer.