Ray Emery took a shutout into the third period and made 18 saves to get the win, Chicago's third in a row. The Blackhawks moved past both St. Louis and Detroit to take the lead in the Central Division.
Toews opened the scoring with 2:20 left in the opening period and Duncan Keith scored on the power play with 17 seconds left in the stanza.
The goal for Toews was his 27th of the season. He is second in the league, four behind Tampa Bay's Steven Stamkos.
Patrick Kane gave Chicago a 3-0 lead in the second and Jason Garrison ended Emery's shutout bid 43 seconds into the third.
Jose Theodore allowed the three goals on 22 shots. Florida has lost four straight.
Chicago will play a home-and-home series with Nashville before embarking on a nine-game road trip over 19 days.