The 2001 track, which spent 49 weeks on the Hot 100 and led the album "Silver Side Up" to multi-platinum status, turns from guitar crunch to piano ballad in Lavigne's hands.
The "Sk8er Boi" singer and Nickelback frontman Chad Kroeger announced their engagement in August. The twosome have been working together closely this year, collaborating on tracks for Lavigne's follow-up to 2011 album "Goodbye Lullaby."
The new cover was recorded for "One Piece Film: Z," a Japanese anime film, for which she's also covered Joan Jett's "Bad Reputation." Lavigne's next release is expected in 2013, with Epic Records chairman Antonio "L.A." Reid telling Billboard in September that the album was "in the mixing process."
Hear her "How You Remind Me" cover below: