Closing in on the first championship of his stellar career, Hasek did not have much to do as he faced only 17 shots. But he made a huge play in the first period, got a lucky bounce in the second and extended his shutout streak to 127 minutes, 13 seconds.
The 37-year-old Hull, whose deflection with 74 seconds left forced overtime in the third game, scored the only goal Hasek needed early in the second period, becoming the fourth player in NHL history with 100 career playoff goals.
The 41-year-old Larionov followed up his triple-overtime heroics with the insurance tally early in the third period. And Shanahan, a youngster at 33, added the clincher with 5:17 to play.
Despite a roster loaded with players on the wrong side of 30, the Red Wings appeared the fresher team coming off the third-longest game in Stanley Cup Finals history. They'll have an extra day off before returning to Detroit on Thursday for the possible clincher in Game Five.
Game Four still was scoreless in the final minute of the opening period when Red Wings defenseman Chris Chelios fell inside his own blue line. That would have allowed rookie Erik Cole to skate unimpeded toward the net, but Hasek charged out to the left faceoff dot and used the paddle of his stick to knock away the puck and keep his shutout streak intact.
Hull joined elite company 6:32 into the second period with his league-leading 10th playoff goal.
Defenseman Fredrik Olausson pushed the puck to Boyd Devereaux at the Carolina blue line, sending him in 2-on-1. Devereaux slid a pass across the slot to Hull, who leaned into a one-timer at the bottom of the left faceoff circle and whipped it off the left goalpost and into the net.
Luc Robitaille, one of Detroit's two other 600-goal scorers, took a retaliatory high-sticking penalty off a faceoff midway through the second period. It nearly led to the tying goal.
Defenseman Bret Hedican, returned to the point on the Hurricanes' power play, blasted a shot from the top of the left circle off Hasek's chest. Jeff O'Neill got the rebound in the slot and quickly flicked it to the right side to Ron Francis, who curled a shot off the far goalpost.
Carolina's power-play struggles continued after Detroit defenseman Steve Duchesne was penalized for holding the stick with 5:26 to go in the period.
For the first time in the series, a team carried a lead into the third period. The Red Wings built on it with 16:17 remaining. Tomas Holmstrom worked the puck up the left boards to rookie defenseman Jiri Fischer, who spotted Larionov at the right goalpost and one-timed a pinpoint pass that the Game Three hero stuffed into the net for his third goal in two games.
Shanahan capped the scoring with just his second goal in 11 games. Sergei Fedorov got a pass from Chelios, drifted into the Hurricanes' zone and cut to the top of the slot before moving the puck to Shanahan, who steered it past goaltender Arturs Irbe for his sixth playoff goal.
Detroit dominated the first scoreless opening period of the series, outshooting the Hurricanes, 10-6, and limiting them to one solid chance through 19 minutes.
Detroit managed just one shot with the man advantage, but Fedorov showed no effects of Saturday's marathon. He had plenty of jump early, whipping a wrist shot from the slot wide of the net, testing Irbe from close range after controlling a pass from Steve Yzerman and firing a slapper from the top of the right faceoff circle.
Carolina's first good chance came with 5:41 to go in the first period. Defenseman Niclas Wallin wristed a shot from the right point through traffic and off the right post.
Hurricanes coach Paul Maurice tried to address two problem areas by juggling his lines. He moved Sami Kapanen, who has one goal in 21 playoff games, off the top line and replaced him with Bates Battaglia, a member of the struggling BBC Line.