The Jayhawks scored on each of their first two drives. Their Air Raid offense then bogged down until gaining possession with 1:03 left in the first half and scoring in three plays.
Junior Steven Sims Jr., the Jayhawks' top returning receiver, scored on a 77-yarder, which came off a quick slant, and a 16-yard bullet across the middle that gave Kansas a 21-7 halftime lead. Sims finished with 142 yards on four receptions.
Picked last in the Big 12 after seven consecutive losing seasons, the Jayhawks expressed more confidence in their offense throughout the preseason stemming, in part, from the hiring of new coordinator Doug Meacham.
The late first-half touchdown seemed to help Kansas hit its stride.
The Jayhawks erupted for two quick scores in the third quarter, including a 57-yard touchdown to tight end Ben Johnson that gave Bender his fourth TD pass.
The last time a Kansas quarterback threw that many touchdowns in a game was Todd Reesing in 2009. Reesing happened to be in attendance as Kansas observed the 10-year anniversary of the Orange Bowl victory that capped an 11-1 run by the 2007 squad.
Bender, who played last season in junior college after playing as a redshirt freshman at Washington State, finished 23 of 37 after competing with Carter Stanley in spring and fall drills. Stanley started the Jayhawks' last three games a year ago, including an overtime win over Texas that ended a 19-game losing streak in Big 12 play.
Southeast Missouri State sliced the lead to 14-7 on a 9-yard touchdown pass from quarterback Jesse Hosket to wide receiver Trevon Billington with 8:52 left in the second quarter.
The Redhawks also used a 45-yard field goal from Nicholas Litang to get within 21-10 early in the second half. Hosket also fired a 22-yard TD to Kristian Wilkerson 2:43 into the fourth quarter.