Meier, who returned to the lineup after missing three games with an upper-body injury, scored his 14th goal of the season.
"It felt great," Meier said. "You don't want to be sitting out watching games with an injury. For me it was important to get healthy. I had a lot of energy today and we played a great game overall."
WATCH: [All Hurricanes vs. Sharks highlights]
Joe Thornton had three assists for the Sharks (14-10-5) to give him 1,038 NHL assists, two shy of tying Marcel Dionne for 10th place on the all-time list.
Barclay Goodrow, Tomas Hertl, Joe Pavelski and Marcus Sorensen also scored, and Kevin Labanc had two assists for San Jose.
"We're coming off the road, I was a little worried about our energy the first game back," Sharks coach Peter DeBoer said. "But we got off to a quick start, got that first goal, which was huge. I thought we had some bounces tonight which we haven't gotten a lot of lately. And [Jones] was great."
Lucas Wallmark scored for the Hurricanes (12-11-4), who lost their third straight game (0-2-1) and have scored two or fewer goals in five straight. Curtis McElhinney made 18 saves.
"We've played good enough to win and we don't get any results," Hurricanes coach Rod Brind'Amour said. "That's hard, it's hard on the guys. It's been a weird year for this. It was a 5-1 game and you think, 'Wow, that's a terrible game.' I didn't see it that way. Maybe I'm wrong, I have to look at it again but it certainly didn't feel like that."