Wyatt Kaiser had a goal, Frank Nazar had two assists, and the Blackhawks (12-9-6) are 4-1-1 in their past six road games. Spencer Knight made 26 saves.
Trevor Moore scored and Darcy Kuemper made 34 saves for the Kings (12-8-7), who have lost six of eight (2-3-3).
Drew Doughty returned for Los Angeles after missing seven games because of a lower-body injury he sustained when he was struck in the foot by a shot against the Ottawa Senators on Nov. 15, and forward Warren Foegele returned after missing three games because of an upper-body injury.
Bedard put Chicago up 1-0 at 6:17 of the second period, charging the crease and sweeping in Tyler Bertuzzi’s centering pass nine seconds into a power play. It was Bedard’s fourth goal and sixth point in his past three games.
Kaiser made it 2-0 at 19:54 on a wrist shot from the slot. Kaiser’s first goal of the season came after the Kings failed to capitalize when the puck got lost in Knight’s skates and Phillip Danault missed a shot on the open net with a wraparound.
Moore cut it to 2-1 at 10:38 of the third period on a wrist shot from the left circle set up by Foegele.
The Kings had a 6-on-4 power play for the final 1:26 after Bedard was called for hooking and they pulled Kuemper for an extra attacker.
Blackhawks forward Teuvo Teravainen left after being hit in the face by a puck with 56.4 remaining.