Demko, who missed 15 games, was activated from injured reserve and played for the first time since Feb. 8, when he sustained a lower-body injury midway through the first period of a 2-1 win against the Toronto Maple Leafs.
"You want to come in and contribute," Demko said. "The guys have been doing so well, competing every night, and you certainly don't want to come in and contribute the wrong way so huge fight from us, coming down to the last minute there and getting the extra point. So I'm just super proud of the team."
Lekkerimaki also scored in regulation for the Canucks (33-26-12), who had lost two in a row and are 2-2-1 in their past five games.
"It was a gut feeling (by goalie coach Marko Torenius) to have Lekkerimaki go in the shootout. That wasn't me," Vancouver coach Rick Tocchet said. "Marko radioed [assistant coach Yogi Svejkovski], ‘Let's go with Lekkerimaki,’ so, obviously, a great choice."
The Canucks pulled within three points of the St. Louis Blues for the second wild card into the Stanley Cup Playoffs from the Western Conference with one game in hand.
Timo Meier scored twice, and Jacob Markstrom made 25 saves for the Devils (37-28-7), who have lost three in a row and are 1-3-1 in their past five.
"It's disappointing, but I love the fight of our team," New Jersey coach Sheldon Keefe said. "I thought we played a good game, but we just made mistakes. On their first and second goals, we exposed the slot area. Normally we do a good job there, but today we gave up too much space and it cost us two goals. I thought our guys played hard and it was a very important point."
New Jersey is third in the Metropolitan Division, seven points ahead of the New York Islanders and New York Rangers.
Suter gave Vancouver a 1-0 lead at 10:09 of the first period on a one-timer from the slot off a pass by defenseman Marcus Pettersson from along the left-wing boards.
"[Suter's] played good hockey," Tocchet said. "I've moved him up and down the lineup from first line to second line and fourth line. He's been everywhere and he's a smart guy; he's actually like another assistant coach for us."