The Wildcats (7-1) hit 92 percent of their foul shots on 22-of-24 shooting. Kamau Stokes added 20 points and Barry Brown 18.
Vanderbilt (3-5) rallied from a 16-point deficit to tie the score with 3:33 remaining on Matthew Fisher-Davis’ 3-pointer, but was outscored 13-3 the rest of the way.
Vanderbilt’s Jeff Roberson added to his Southeastern Conference lead with his fifth double-double by scoring 22 points and grabbing 10 rebounds. Saben Lee added 19 points, including 12 at the free-throw line, and Joe Toye scored 11.
Vanderbilt’s Riley LaChance fouled out after being hit with a double technical foul with 7:38 left. He exited with nine points after erupting for a career-high 27 in Tuesday’s 74-62 win over Radford.
After trailing by as many as 16 in the first half, Vanderbilt made a 10-0 run to cut the deficit to 58-57 on LaChance’s 3-pointer with 9:15 remaining in the game.
K-State, whose only loss was a 92-90 setback to 20th-ranked Arizona State on Thanksgiving night, shot 62 percent in the first half to seize a 43-30 lead.
Vanderbilt started cold, missing 14 of its first 21 shots from the field.