The Bears (7-4, 4-3 Southland) built a 21-0 first-quarter lead on a 6-yard run by Dick, a 69-yard scoring pass from Dick to Isaiah Jackson and a 36-yard fumble return by Markell Carter.
McNeese State (6-5, 5-2) pulled within 21-14 in the high-scoring first quarter, got a 42-yard field goal from Josh Lewis in the third and took their first lead with 7 minutes remaining when Jacob Bower hit Wes Briscoe with a 10-yard touchdown pass.
Robey erased that with his late TD and finished with eight catches for 103 yards. Jackson had five receptions for 115 yards while Dick completed 22 of 34 passes for 291 yards.
Bower was 18 of 36 for 192 yards with two touchdowns and two interceptions. Andre Anderson had 101 yards rushing for McNeese State.