Kane made it 2-0 on a wrist shot from the right circle at 13:48. It was Kane's 16th point (six goals, 10 assists) in 19 games with San Jose since being acquired in a trade with the Buffalo Sabres on Feb. 26. Suomela and Joonas Donskoi had the assists.
Kopitar made it 2-1 at 17:15. Derek Forbort's shot redirected off Alex Iafallo across the face of goal, and Kopitar got it at the back post.
"Once [we] got the first goal, we just kind of settled down and started making plays," Kopitar said. "Unfortunate to only get a point out of it, but I think we should be encouraged from this game. Obviously there is some stuff to work on, but it's the first game of the season, so not everything is going to be perfect."
San Jose was 0-for-3 on the power play for the second consecutive game. Los Angeles was 0-for-5 despite winning seven of nine face-offs.
"Sometimes we can't even get in the zone, it's unacceptable," Kovalchuk said. "(Coach) John [Stevens] put us out there. He believed in our skill and our willingness to do the right things, and we have to do it to be able to win."