MANHATTAN, Kan. (AP) _ Larry Reid scored 31 points and Kansas State beat No. 19 Iowa 86-78 Saturday night for its first victory over a Top 20 opponent in almost seven years.

Phineas Atchison sank four straight free throws in the final 20 seconds as the Wildcats withstood a late rally by the Hawkeyes (9-1), who were playing their second road game and first outside the state of Iowa.

After Richie Terry's free throws made it 82-74, Iowa's Dean Oliver drove in for a layup to slice the lead back to six. Ryan Hogan got it to 82-78 with a driving layup, but Kansas State got the last four points at the line.

Kansas State (5-4), projected to finish last in the Big 12 a second straight year, had not beaten a Top 20 team since upsetting No. 1 Kansas 68-64 on Jan. 17, 1994. No ranked non-conference opponent had lost at Kansas State since No. 8 Minnesota got beat 62-52 in 1981.

Iowa got to 70-63 on Glen Worley's bucket with about three minutes left. Reid then hit a free throw and after a furious flurry under the bucket, Quentin Buchanan brought the half-filled coliseum to its feet with an uncontested dunk that made it 73-63.

Iowa's Reggie Evans, the nation's leading rebounder, had his 10th straight double-double with 18 points and 18 rebounds. Evans was 12-of-19 from the foul line. Luke Recker had 25 points for Iowa.

The Hawkeyes got off to a miserable start, missing their first nine shots while getting five field goal attempts blocked by the energized Wildcats.

Glen Worley finally stopped the drought with a 15-footer and a few minutes later consecutive 3-pointers by Hogan cut the deficit to 8-7. Iowa shot just 28 percent in the first half as the Wildcats took a 30-22 lead at halftime.