Albrecht did not attempt a field goal in his first two seasons and was limited to six extra points in a season-opening 42-19 victory over Southern last week.
The Ragin' Cajuns, unbeaten through their first two games for the first time since 1990, trailed 15-14 before driving from their 33 to the Kansas State 30. Louisiana-Lafayette had only two first downs in the second half before quarterback Chris Masson completed four passes for 30 yards in the final drive.
Kansas State (1-1) rallied from a 14-2 deficit with two fourth-quarter touchdowns.
Seven minutes later, Thomas capped an 86-yard drive with a 3-yard run, and Josh Cherry hit the extra point for the 15-14 lead with 8:08 left.
Thomas finished with 136 rushing yards, 92 in the second half.
The Wildcats took a 2-0 lead when Masson ran out of his own end zone after a bad snap with 2:43 left in the opening quarter.
Masson, who finished 20-for-36 for 185 yards, came back to guide the Ragin' Cajuns on a 61-yard drive that was capped by Undrea Sails' 9-yard touchdown run with 9:37 left in the first half.
Louisiana-Lafayette drove 73 yards in the final 2:19 of the half to take a 14-2 halftime lead on Masson's 1-yard pass to Luke Aubrey.
The Ragin' Cajuns had three first-half turnovers, but the Wildcats couldn't take advantage despite having five first-half possessions in Ragin' Cajun territory. Kansas State was 0-for-8 on third-down conversions in the first half.