Reimer preserved the shutout with a glove save against Jake McCabe in the final minute of the second period and nine saves in the third.
Meier scored an empty-net goal with 1:31 remaining for the 2-0 final.
"We had a game plan that we didn't stick to in the first period, came out a little bit flat and weren't winning enough battles, but our compete in the second and third was much better," Sharks defenseman Mario Ferraro said. "We're the kind of team, we have to play physical, we have to play hard, so if we take a period off it's going to hurt us. So, 'Reims' kept us in there for sure."
The Sharks blocked 32 shots, led by Ferraro (seven).
"They did a good job defensively, for sure," Blackhawks forward Patrick Kane said. "Not just blocking shots, but also just getting pressure on the puck and keeping us to the outside. Got to give them credit."
Chicago was 0-for-2 on the power play and is 0-for-13 over its past six games.
"It's just amazing, you know, especially going through training camp and the beginning of this season, we were so confident, so comfortable on the power play," Kane said. "It's one of those stretches where, I think, we had chances before and we didn't score. Then all of a sudden you get one, two power plays a game, you kind of get out of rhythm and you don't do your job when it comes up.
"Hopefully we can get it going again and get that confidence like we had at the beginning of the season."
NOTES: It was Reimer's 25th NHL shutout and fourth with the Sharks. … With his two goals, Meier has 20 points in 16 games this season. The only players in Sharks history to score 20 points in fewer games are Joe Thornton (13 games in 2005-06), and
Patrick Marleau
(15 in 2009-10). … Blackhawks forward Alex DeBrincat had his eight-game point streak end. … Chicago forward Dylan Strome was scratched for a second straight game.