Krajicek took a shot from the left circle that went over the glove and shoulder of Nashville goalie Tomas Vokoun 2:32 into the extra period.
Jan Bulis, Taylor Pyatt, and Brendan Morrison scored for Vancouver, which won for the third time in four games. Roberto Luongo stopped 37 shots for the Canucks.
Scott Hartnell, J.P. Dumont and Martin Erat had the goals for Nashville, which had its four-game winning streak snapped.
Erat capitalized on a two-on-one break to put the Predators ahead 3-2 at the 6:40 mark of the second period.
However, Morrison tied the score at 18:20 of the third, taking control of the puck in a crowd of players battling for the rebound and putting the puck in the open net as Vokoun had positioned himself at the front of the crease.
Vancouver took a 1-0 lead one minute into the game when Bulis fired a shot from the middle of the left circle that went past Vokoun's stick.
Hartnell tied the score at 5:55 with a shot that bounced off Luongo and went into the net.
Vancouver wanted to get more traffic front of the net against the Predators. Pyatt spent most of the game camped out in front of Vokoun, and was able to find an opening at 16:13 of the first period.
The Predators refocused in the second period, and sending 19 shots at Luongo. Dumont tied the score on a two-on-one break at 3:35.
Vokoun finished with 42 saves.
Notes: Rookie Alexander Radulov made his debut for Nashville, alternating between lines and getting his first penalty at 11:06 of the third period for tripping. ... Erat, who has points in his four of his last five games, took over the scoring lead with four goals and four assists. ... Vancouver's Sami Salo, picked up an assist to add to his points total (three goals, four assists) as the team's leading defencemen. ... The Predators have beaten Vancouver four consecutive games dating back to March 2, 2006. ... With Steve Sullivan sidelined for the second game in a row with back problems, Jason Arnott has been serving as an assistant captain.