Thompson also returned a punt 61 yards to the Ragin' Cajuns' 1-yard line in the third quarter to set up a touchdown run by Jake Waters. Zimmerman's interception return moments later gave Kansas State touchdowns on offense, defense and special teams in a span of minutes.
Waters threw for 278 yards while splitting time with backup Daniel Sams, who ran for 63 yards and a touchdown. Tyler Lockett had eight catches for 111 yards, and John Hubert ran for two touchdowns as the Wildcats avoided their first 0-2 start since 1989.
Terrance Broadway ran for a touchdown and threw for a touchdown for the Ragin' Cajuns (0-2), and Darryl Surgent returned a kickoff a school-record 100 yards for another score.
Both teams began the season with lofty aspirations, and both trying to rebound from season-opening disappointments -- the defending Big 12 champion Wildcats lost at home to North Dakota State last Friday night, and Louisiana-Lafayette fell 34-14 at Arkansas last Saturday.
Both got off to slow starts this week, too.
Kansas State finally got in gear after the teams traded field goals, and Hubert capped a 71-yard drive with a 7-yard scamper. The Ragin' Cajuns failed to pull off a fake punt on their ensuing possession, and Sams finished another TD drive with a hip-swiveling 13-yard run to make it 17-3.
Jack Cantele's second field goal of the half gave Kansas State a 20-3 lead at the break.
The real fireworks came early in the third quarter.
Thompson fielded the opening kickoff of the second half, made a couple of nimble moves up the Louisiana-Lafayette sideline and raced the rest of the way to the end zone. The return gave Kansas State at least one kickoff return touchdown in a nation-leading nine straight seasons.
Thompson's big punt return and Waters' TD plunge gave Kansas State a 34-3 lead.
The Ragin' Cajuns answered with Surgent's kickoff return and an interception by Dominick Jones later in the third quarter set up Broadway's touchdown run and got them within 34-17.
Louisiana-Lafayette got the ball back quickly, but momentum swung back to Kansas State when Zimmerman caught a tipped pass over the middle and returned the pick for a touchdown. It was the senior's 11th career interception, moving him into sixth place in the school record books.
Broadway tried to rally the Ragin' Cajuns once more, hitting Robinson from 18 yards out for a touchdown late in the third quarter. After getting the ball back, their next drive stalled and they had to settle for Stephen Brauchle's 26-yard field goal to get within 41-27 with 10:55 left.
Kansas State put the game away when Sams, taking over for Waters, hit tight end Zach Trujillo for a 27-yard gain. The speedy Sams then ripped off three long runs to set up Hubert, the 5-foot-7 wrecking ball, who powered into the end zone for his second touchdown.