The Blackhawks moved into a tie with San Jose for the highest point total in the Western Conference.
Chicago faced a 2-1 deficit when Dave Bolland scored on a backhander with 1:57 to go in the second period.
Hjalmarsson then started Chicago's big third period with a slapshot that got past Devan Dubnyk. Dustin Byfuglien and Jonathan Toews also scored in the third period to give the Blackhawks their fifth win in six games.
Cristobal Huet had to make just 12 saves to get the win.
Edmonton has lost seven out of eight and has the worst record in the West.
Chicago won all four meetings with Edmonton this season. That had not happened in 15 seasons.