With Canucks No. 1 goalie Roberto Luongo getting the night off, the rookie Swede picked up his fourth win of the season in his first-career appearance at Rogers Arena.
Justin Peters made 24 stops for Carolina (13-13-5), which saw its three-game winning streak snapped.
After Tanev gave the Canucks a 1-0 lead in the first period, Lack was steady the rest of the way as Vancouver kept Carolina to the outside most of the night.
He made two glove saves early in the third period, the second coming on a hot shot off the stick of Hurricanes forward Nathan Gerbe.
Carolina made a push in the dying minutes, with Hurricanes captain Eric Staal coming the closest, but Lack was there to the shut the door before Hansen scored into an empty net.
Lack (4-2-0) usually plays the second game of back-to-backs in place of Luongo and got the nod from Canucks head coach John Tortorella with Monday's contest coming on the heels of Sunday 3-1 home victory over the Colorado Avalanche.
The 25-year-old Lack's last start came in the Canucks' 3-2 victory over the Hurricanes in Raleigh, N.C., on Dec. 1 and he watched as Vancouver gave him a 1-0 lead early in the first on Monday night.
Tanev collected a feed from fellow defenceman Dan Hamhuis and fired a snapshot from the point that found its way through traffic past Peters at 3:35 for his second of the season.
Hamhuis then jumped into the rush with Canucks shorthanded, but fired wide of Peters' goal. Then with Vancouver still down a man, Peters was forced to make a pad stop on Kesler, two more saves on Hamhuis and then another on Henrik Sedin as the Canucks' No. 1-ranked penalty killing unit buzzed around the Hurricanes' zone.
The visitors started to find their legs in the second period, but found it difficult to get much going against the tight-checking Canucks.
Hurricanes forward Tuomo Ruutu couldn't find the range against Lack from in tight midway through the period as Carolina's 27th-ranked power play sputtered.
Former Canucks forward Manny Malhotra played in Vancouver for the first time as a the member of the Hurricanes. The Canucks shut Malhotra down after nine games last season, saying they were concerned for the 33-year-old's health following a serious eye injury during the 2010-11 season.
Malhotra got an American League Hockey tryout with Carolina's affiliate this season before getting called up to the big club. He made his debut Nov. 1 against the Tampa Bay Lightning.
Notes: The Canucks don't play again until Friday when they welcome the Edmonton Oilers. Vancouver then hosts Boston on Saturday night. It will mark the Bruins' first visit to Rogers Arena since their victory in Game 7 of the 2011 Stanley Cup final. ... Carolina plays at Edmonton on Tuesday.