Tristan Jarry made 27 saves for Pittsburgh (37-21-6), which remains one point behind the Philadelphia Flyers for second place in the Metropolitan Division.
"I think we understand what it takes to win," Penguins center Sidney Crosby said. "But I put it on myself. I've got to step up. Key situations, you're down like this and losing games, you need big plays, big performances, and I haven't done that."
The Penguins have been outscored 24-8 in the streak. They last lost six straight in regulation from Dec. 29, 2011 to Jan. 11, 2012.
"We have to try to understand it's not easy to win and it doesn't matter who you play," Penguins forward Evgeni Malkin said.
Kane scored his 22nd goal of the season on a breakaway at 18:48 of the first period for a 1-0 lead. Marc-Edouard Vlasic sprung Kane, who fought off a slash from Pittsburgh defenseman Marcus Pettersson to score on the delayed penalty.
"I just saw some space," Kane said. "Vlasic made a nice play to move it up the middle right away and I was able to split the defense."
Meier made it 2-0 at 11:12 with his 21st goal.