Jarnkrok scored after carrying the puck into Vancouver's zone, skating around Canucks forward Sam Gagner and shooting from the high slot.
The Predators overcame a 2-0 deficit for the second night in a row. The Canucks took their second straight overtime setback at home.
Mike Fisher, in his first game since officially coming out of retirement Monday, Kevin Fiala and Ryan Ellis tallied for Nashville in regulation.
Daniel Sedin led the Canucks with a goal and an assist. Bo Horvat and Brandon Sutter also scored for Vancouver. Alex Edler assisted on two of the hosts' goals, becoming the franchise's all-time points leader among defensemen with 326.
In an unusual moment, Edler received a brief salute from the crowd as his accomplishment was announced in the break before overtime. He waved to the crowd in appreciation, but the good feelings ended quickly as Jarnkrok emerged the hero.
Daniel Sedin put in his own rebound at 11:54 of the third period to give the Canucks a 3-2 lead. However, Ellis forced overtime as he fired a slap shot in off a Vancouver defenseman's leg with 2:15 left in the final frame.
"It's tough to lose (the lead) that late in the game," Sedin told Sportsnet.
Nashville backup netminder Juuse Sartos blocked 24 of 27 shots for the win. Vancouver goaltender Jacob Markstrom recorded 39 saves.
The Canucks scored on two of five power plays, while the Predators were blanked on both of their man-advantage chances. However, Nashville was able to triumph despite dealing with a five-minute major in the third period.
Markstrom was steady two nights after allowing three goals on five shots in 12:29 of work against the New York Rangers.
Horvat opened the scoring on a power play 5:55 into the game as he deflected in Alex Edler's point shot. Daniel Sedin, 37, earned an assist on the play, extending his points streak to five games.
Sutter gave the Canucks a 2-0 advantage 15:04 into the second period as he put in a high backhand while cutting across the slot and falling to his knees.
Fisher put the Preds on the scoreboard at 17:26 of the middle period when he spun around and whipped in a long rebound of a Filip Forsberg shot.
The Predators lost top center Ryan Johansen at 9:28 of the third period as he was ejected for spearing Vancouver defenseman Erik Gudbranson. Johansen was handed a five-minute major as well as his game misconduct. However, the Canucks did not go on the power play immediately, because Sutter received a roughing penalty for tussling with Johansen after the spearing incident.
With the teams playing four-on-four, the Canucks inexplicably left Fiala alone and he fired in a pass from Kyle Turris at 10:02.
--Field Level Media
Nashville | Vancouver | |
Ryan Ellis 2 | Points | Daniel Sedin 2 |
Ryan Ellis 1 | Goals | Daniel Sedin 1 |
Viktor Arvidsson 2 | Assists | Alexander Edler 2 |
N/A | Power Play Goals | Daniel Sedin 1 |
N/A | Short Handed Goals | N/A |
Juuse Saros .889 | Save Percentage | Jacob Markstrom .907 |
Juuse Saros 24 | Saves | Jacob Markstrom 39 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Nashville | 43 | 4 | 0-2 | 3-5 | 21 | 37 |
Vancouver | 27 | 3 | 2-5 | 2-2 | 6 | 30 |