Thomas turned in 27 saves and shut out the Canucks in the shootout to nail down Florida's first victory in Vancouver since 1994 and their third in their last four games.
Thomas led the Boston Bruins to victory in the 2011 Stanley Cup finals against Luongo and the Canucks.
Luongo finished Tuesday's tilt with 34 saves, but he failed to stop Jonathan Huberdeau from scoring the only goal in the shootout. As a result, Vancouver's winless streak was extended to five games, the longest since 2009.
Brad Boyes and Shawn Matthias scored in regulation for Florida. Matthias' goal at 8:34 of the third period tied the score 2-2.