Versteeg scored twice in the opening period and added an empty-net goal with 1:19 left in the third as part of Florida's second straight win. Winnipeg has lost four in a row.
The Panthers took a 4-0 lead through two periods with Jason Garrison and Mike Santorelli scoring in the second.
Versteeg's first goal came on a tip-in of a shot by Tomas Fleischmann 7:14 into the game and he produced a power-play score with 2:33 to go in the opening stanza. Versteeg is in his first year with Florida after spending three seasons in Chicago and one in Philadelphia.
Jose Theodore made 25 saves in the victory.
Ondrej Pavelec opened in goal for the Jets and was beaten four times on 15 shots through two periods. Peter Mannino turned aside the four shots he faced in the third.