Toews broke a 1-1 tie with 3:22 remaining in the second period when a Viktor Stalberg shot bounced off the backboards directly to where he was standing alone at the side of the goal.
The Blackhawks captain quickly fired it home into an empty net for his team-best 13th goal and Western Conference-leading Chicago hung on to finish a six-game road trip with a 3-3-0 mark.
Jarrett Stoll tallied an unassisted goal for the Kings' only score and Jonathan Quick made 25 saves for Los Angeles.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Kate Middleton recycles dress at movie premiere