Joey Kocur, Igor Larionov and Darren McCarty scored for the defending Stanley Cup champions. The Red Wings are 4-0 for the first time since the 1972-73 team won its first six.
Osgood has given up only four goals in the Red Wings' four wins. He is 4-0 against Tampa Bay in his career.
"I'm just getting a lot of breaks now, and the team's playing well in front of me," Osgood said. "There may be stretches during the season when it doesn't go this well, but if you get off to a good start, it builds confidence and you carry that through the season."
Corey Schwab, making his first start of the season in Tampa Bay's goal, made 32 saves.
Kocur scored his first goal of the season 4:21 into the second period when he skated backward to the left circle to gain control of a pass from Brent Gilchrist, then fired a shot between Schwab's legs.
Larionov made it 2-0 in the third period when he took a pass from Nicklas Lidstrom to the right of the net and slipped it behind Schwab at 11:35. Detroit's Larry Murphy got his 800th career assist on the play.
"I think this was our best game, especially in the second half," Detroit Coach Scotty Bowman said. "We had our best tempo and we created a lot of chances."
Carolina caught a break on Leach's game-winner when Martin Brodeur--one of the best goaltenders in the NHL--misplayed the initial shot from Robert Kron just inside the blue line.
Kron's blast appeared to be wide, but Brodeur tried to stop the high shot with his blocker. It bounded out of control, to his left and onto the stick of Leach, who was streaking down the slot and slammed the puck into the open net.
"I misplayed it," said Brodeur, one of the NHL's best goaltenders the past four seasons. "I should have probably just tried to hold on to it and I tried to direct it and it kind of moved on me. It hit the side of my blocker. It's unfortunate but it happens."
The former Hartford Whalers opened the scoring 13:58 into the first period. Jeff O'Neill outraced Devil defenseman Ken Daneyko for the puck along the left boards, fired it to Sami Kapanen in the slot, and his touch pass to Geoff Sanderson left him with a wide open net.
Randy McKay's fourth goal of the season, 58 seconds into the third period, tied it at 1-1.
Chicago (0-4-0) is off to its worst start since the 1969-70 season.
"There was a lot more room out there than there usually is against that team," said Modano after his fourth career hat trick. "You never expect an open-ice game against them. But we got a couple of quick goals in the second period and the floodgates opened. They're a totally changed team. It's going to be a tough year for them, I think."
Joe Nieuwendyk added two goals, Todd Harvey had a goal and an assist, and Darryl Sydor had two assists as the Stars improved to 2-2-1.
Belfour was the Blackhawks' goaltender from 1989 until he was traded to San Jose last season. Belfour, who signed a three-year, $10 million free agent contract with the Stars in the off-season, was seldom tested by the punchless Blackhawks in his 32nd career shutout.
"We're not getting very much done," Chicago Coach Craig Hartsburg said. "Right now we're a disfunctional team and we've got to fix it."
The Chicago Blackhawks acquired right wing Martin Gendron from the Washington Capitals for a fifth-round pick in the 1998 draft. The Blackhawks also received Washington's 1998 sixth-round draft pick. . . . Philadelphia Flyer left wing John LeClair will likely sign a new contract within the next few days, his agent said.