San Jose had charged back from a two-goal deficit with late tallies from Andrew Desjardins and Joe Pavelski, forging a 3-3 a tie with 5 minutes left.
But Columbus regained the lead when Pavelski coughed up the puck at his own blue line and Johansen skated in on Antti Niemi, unleashing a shot to his blocker side for the game-winner.
Vinny Prospal supplied a goal and an assist while Sergei Bobrovsky stopped 32-of-35 shots for Columbus, which pulled into a tie with Minnesota for the seventh and eighth Western Conference playoff seeds with 51 points apiece.
Martin Havlat also scored and Niemi ended with 18 saves for the fifth-seeded Sharks.
Swim Week Miami Beach 2014 [PHOTOS]