Johansson signed a two-year contract with Tampa Bay on July 1.
Anthony Cirelli scored twice, and Felix Robert had a goal and an assist for the Lightning.
Yaniv Perets made 24 saves for the Hurricanes, who used a split squad.
Cirelli made it 1-0 at 16:57 of the first period after intercepting the puck on the forecheck, and Robert pushed the lead to 2-0 at 13:06 of the second period.
Cirelli extended it to 3-0 with a short-handed goal at 14:05 of the third, and Luke Glendening made it 4-0 at 15:45.
