The last time they has this good of a road run was a five-game spurt from Oct. 22-Nov. 14, 2005, during Carolina's Stanley Cup championship season.
The Hurricanes, ninth in the Eastern Conference, started the day five points below the postseason cutoff. Ray Whitney, Dennis Seidenberg and Sergei Samsonov added goals, and Cam Ward stopped 22 shots.
Islanders defenseman Mark Streit scored for the third time in his last four games, but New York dropped both ends of back-to-back games - including a 3-1 road loss to the New York Rangers on Wednesday.
Jon Sim also scored, and Joey MacDonald made 24 saves for the Islanders, who had won four of six home games (4-0-2), but own the NHL's worst record (17-35-6). New York has lost seven of eight overall (1-6-1).
Whitney gave Carolina a 1-0 lead 5:23 in when he deflected Anton Babchuk's left-point shot past the ineffective MacDonald. Streit tied it with a power-play goal at 11:48, but that was the last bit of positive play from the Islanders.
Cullen put Carolina ahead for good after Whitney found him alone in the slot. He calmly shifted the puck from backhand to forehand and swept in a shot. Staal made it 3-1 by turning a pass from Samsonov in the left circle into a drive over MacDonald's right shoulder with 2:51 left in the first.
Islanders defenseman Bruno Gervais nearly brought his club within a goal early in the second, but for the second straight night was turned aside by the goal post.
Staal got back on the board with 3:11 remaining in the second, off another assist from Samsonov, and Seidenberg pushed the lead to 5-1 with 15.4 seconds left.
Samsonov and Sim traded goals in the third period.
Notes: Staal has six goals and three assists in his last seven road games. ... Islanders RW Richard Park will be out four weeks due to broken ribs. Park had played in 223 consecutive games. ... New York RW Trent Hunter (hip flexor) returned after missing four games. ... The Hurricanes haven't matched their road success at home, where they have lost three straight and were outscored 15-2. They hold a 20-7 scoring edge during their road-winning streak.