Legwand, Jason Arnott and J.P. Dumont each finished with a goal and an assist for the Predators, who have won two straight on the heels of a three-game skid. Martin Erat collected three helpers and Dan Hamhuis finished with two, while Pekka Rinne stopped 29-of-32 shots to earn the win.
Dustin Byfuglien, Martin Havlat and Patrick Kane each tallied for the Blackhawks, who were coming off Sunday's 2-1 home loss to Minnesota that snapped a four-game win streak. Cristobal Huet yielded five goals on 29 shots in defeat.
Trailing 3-1 after 40 minutes of play, Legwand lit the lamp at 2:10 of the third period and Dumont tied the game three minutes later on the power play.
Joel Ward put the home team in front for good with 5:03 remaining. As Legwand drove hard to the net, Erat let fly a shot from the high slot that was stopped by Huet. Ward followed up the play and poked in the rebound.
Shea Weber added a power-play goal with 2:50 left in the game to seal the come-from-behind win.
After a fruitless opening frame, Byfuglien put the visitors on the board at the 6:05 mark of the second period. Havlat then found the back of the net at 8:57 for a 2-0 Chicago lead.
Arnott shaved the deficit in half, backhanding the rebound of a Steve Sullivan shot under the crossbar with 5:49 remaining in the middle stanza. The Blackhawks, though, regained a two-goal advantage 66 seconds later when Kane's bid from a sharp angle banked off the side of Rinne.