Jeff Withey had 17 points and 13 rebounds, Ben McLemore added 14 points and No. 9 Kansas used another big first-half run to help put away Richmond, 87-59 on Tuesday night.
Travis Releford and Naadir Tharpe each added 11 points, and Elijah Johnson had seven assists for the Jayhawks (9-1), who will ride an eight-game win streak into Saturday's showdown at No. 7 Ohio State — a rematch of last year's national semifinal won by Kansas.
The Jayhawks used an 18-0 first-half run to bury the Spiders, allowing them to push their home winning streak to 28 games, tied for the sixth-longest in school history.
Derrick Williams had 14 points and Cedrick Lindsay finished with 12 for the Spiders (9-3), who had been 7-3 in their last 10 games against ranked opponents.
The Jayhawks had an easier time with Richmond than the last time the teams met at Allen Fieldhouse. In January 2004, the Spiders waltzed into one of the most intimidating environments in college basketball and beat Kansas with a jumper in the final second.
It's one of the seven home losses in coach Bill Self's 10 seasons at Kansas.
Their game Tuesday night never had the same kind of drama.
Richmond appeared stunned by the boisterous crowd of 16,300 in the opening minutes, allowing the Jayhawks to get out to a quick lead. The Spiders' 3-point shooting allowed them to crawl within 15-11 with 11½ minutes left before everything suddenly went cold.
Johnson started the Jayhawks' big scoring binge with a third-chance basket, McLemore buried his second 3 of the half and fellow freshman Perry Ellis scored inside. On the next possession, McLemore scored and went to the foul line, missed the free throw and watched as Ellis put it back for a four-point trip and a 26-11 lead with 8:20 remaining on the clock.
Withey got into the act with a bucket and then a three-point play, and Johnson finished off the 18-0 run with a couple of free throws that made it 33-11 with 4:26 to go.
Williams, a burly junior forward, provided the basket that ended the Spiders' 8-minute-plus drought, and two more baskets by Richmond trimmed the lead to 15 points.
It was the closest the Spiders would get the rest of the way.
Kansas answered with another four-point trip — Withey scored and missed his foul shot, and Kevin Young was there for the follow. And then with 1.5 seconds left, Releford went to the foul line and made good on both of his free throws, getting a second chance after missing the second when Williams was called for a lane violation.
It all amounted to a 39-18 lead at halftime, with the Jayhawks shooting 57 percent from the field and holding a 24-10 edge on the glass.
The Jayhawks were merely in it for style points in the second half, at one point putting together another 18-2 run that made it 73-35 with 5:21 left. Kansas went through the motions down the stretch as it started to turn its attention toward the Buckeyes.
Kansas beat Ohio State at Allen Fieldhouse early last season before beating the Buckeyes again in the Final Four. The Jayhawks lost to Kentucky in the national title game.