JaCorey Shepherd caught three passes for 107 yards and two touchdowns. He went 56 yards for one score and then, after getting wide open on a fourth-and-3 play in the fourth quarter, hauled in a 48-yard pass for another.
Kansas also got touchdown runs from James Sims, who totaled 104 yards on 19 carries, and Tony Pierson.
The Jayhawks looked snappy and much faster than last year, when they struggled to a 3-9 finish in Gill's first season, beginning with a shocking 6-3 loss to Division II North Dakota State.
Webb, who started seven games in an injury-marred 2010 season, attempted only 10 passes, but completed seven for 146 yards.
Pierson, a true freshman, went 47 yards on his first carry to set up a touchdown and 13 yards into the end zone the second time he touched the ball. He had 73 yards on five carries.
Cody Stroud was 22 for 27 for 210 yards and a touchdown for the Cowboys. He alternated with Riley Dodge, who was 9 for 14 for 107 yards and another TD.
After getting stopped cold on their first possession, the Jayhawks went 84 yards in eight plays on their second, with Webb hitting Daymond Patterson on a 25-yard scoring pass following Sims' 30-yard scamper up the middle.
The Jayhawks took a 21-3 lead into halftime following Sims' 1-yard touchdown run and Pierson's 13-yard carry out of a wildcat formation.
The Cowboys scored on their first possession of the second half, rolling 76 yards in 12 plays. Stroud flipped a short pass to Champlain Babin, who got two excellent blocks while going into the end zone. Babin had five catches for 108 yards.
The Jayhawks answered with Shepherd's 56-yard catch-and-run. Shepherd and Kale Pick seemed to be running the same route, and both had their hands up. But Shepherd, a couple of steps behind Pick, was the one who pulled in the ball.
McNeese State's Dodge, on fourth-and-14, found a wide-open Wes Briscoe for a 32-yard scoring pass in the third quarter. Then back came the Jayhawks, with Sims getting a short touchdown run for a 35-16 lead early in the fourth.
Stroud connected with Babin on a 60-yard pass play, then got into the end zone two plays later. He hit Damion Dixon for a two-point conversion that made the score 35-24 with 8:32 to go before Webb hooked up with Shepherd on another long scoring pass.