Legwand put back his own rebound after Jean-Sebastien Giguere made the initial save.
Pekka Rinne gave up two first-period goals and then blanked the Avalanche the rest of the way while Nashville was rallying to its third straight win.
Legwand started the comeback midway through the second period and Sergei Kostitsyn tied it 8:48 into the third. Colorado built its early lead on goals by Ryan O'Reilly and Gabriel Landeskog.
Rinne stopped 27-of-29 shots.
Giguere made 35 saves for Colorado, which has dropped three in a row.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff