The Jayhawks (9-0) led 42-27 at the half, then built their advantage to 71-51 on the second of back-to-back 3-pointers by Henry with 6:33 left in the contest.
Their largest margin was the final score.
Cole Aldrich had 19 points, while Markieff Morris had 12 points and 12 rebounds, and Tayshawn Taylor scored 10 points with six assists in the Jayhawks' big win before 18,000 fans at Kansas City's Sprint Center.
Jerrell Williams and Rodney Green led LaSalle with 21 and 19 points, respectively. Yves Mekongo finished with 10 points, nine rebounds and six assists for the Explorers (6-3), who had won three in a row.