Soon after, Cheveldae was traded and a dynasty was born.
Osgood, 38, announced his retirement Tuesday after 17 seasons in the NHL. He leaves the ice a three-time Stanley Cup champion with 401 career victories, which ranks 10th all-time in the NHL and second in Red Wings' history behind Terry Sawchuk.
Osgood will stay in the Red Wings' organization as a goalie consultant and will work with the organization's young prospects.
He'll be eligible for induction into the Hockey Hall of Fame in 2014, when there will certainly be debates on if he's worthy.
At the very least, Osgood belongs in the discussion.
While he wasn't always the No. 1, Osgood was around for the better part of Detroit's dynastic run of four Stanley Cup championships from 1997-2008. He was the starter on the 1998 squad that swept Washington in the Stanley Cup Final and also the No. 1 goalie on the 2008 team that beat Sidney Crosby and the Pittsburgh Penguins in six games to win the franchise's 11th championship.
Osgood missed out on the Wings' 2002 championship, as he was selected by the Islanders in the 2001 waiver draft and played most of two seasons in New York before being traded to St. Louis.
Save for a stretch from 2001-04, when Osgood split 179 appearances between the Islanders and Blues, he was a Red Wing.
Osgood appeared in 565 games over his 14 seasons with Detroit. He had to win the No. 1 job on several occasions, but almost each time he was up for the challenge.
His first came as a rookie in 1993-94, when he played so well that then Red Wings' GM Jim Devellano moved to trade Cheveldae, who was only 26 years old, to the Winnipeg Jets to make room for Osgood to take the bulk of the ice time.
Osgood went 23-8-5 in 1993-94, but he couldn't help the favored Wings beat San Jose in the first-round of the playoffs. Detroit signed ex-Calgary Stanley Cup-champion goalie Mike Vernon in the offseason and made him the No. 1 for the lockout shortened 1994-95 season.
Vernon led the Red Wings to their first Stanley Cup Final in 29 years. They were swept by New Jersey.
Osgood regained his No. 1 job in 1995-96 and finished the season with an NHL-best 2.17 GAA and 39 victories to become a finalist for the Vezina Trophy. Detroit lost to Colorado in the Western Conference Finals.
Osgood handled the majority of the playing time in 1996-97, but Vernon was named the Wings' No. 1 goalie for the playoffs and led them to the first of four Stanley Cup championships in an 11-year run.
However, the Red Wings just couldn't pass up the opportunity to give Osgood another shot the following season, so they traded Vernon to San Jose. Osgood, who was still only 26 years old, led the Red Wings to a second straight Cup championship in 1998.
No team has repeated as Stanley Cup champions since those Red Wings.
Osgood held his job as Detroit's No. 1 goalie for the next three seasons, but his win totals dropped from 34 to 30 to 25 and Red Wings' GM Ken Holland decided to go in a different direction. He signed Dominik Hasek and eventually left Osgood unprotected in the waiver draft.
The Islanders selected him with the first pick and quickly made him their No. 1 goalie ahead of Garth Snow. Osgood played 103 games as an Islander and helped them reach the 2002 playoffs before he was shipped to St. Louis on March 11, 2003.
The Islanders had drafted Rick DiPietro with the No. 1 pick in the 2000 Entry Draft and felt it was time to give him a chance to claim the No. 1 job.
Osgood spent the 2003-04 season in St. Louis, appearing in 67 games and helping the Blues reach the playoffs, but he became a free agent going into the work stoppage.
When the NHL returned, Detroit wanted him back. Osgood returned to Hockeytown on a two-year contract to work side-by-side with Manny Legace. Groin injuries hampered him in the 2005-06 season and with the Wings bringing Hasek back in 2006-07, Osgood was again a backup.
However, he picked up more playing time in 2007-08 because while he was playing well, Hasek was struggling and eventually suffered an injury. Osgood led the NHL with a 2.09 GAA that season, but it wasn't good enough to become the No. 1 goalie to start the playoffs.
Detroit coach Mike Babcock instead went with the healthy Hasek to start the first-round series against Nashville, but it was the wrong move. Hasek was ineffective and Babcock quickly realized he'd better make a change or the favored Red Wings, the Presidents' Trophy winners, could be facing an early elimination.
Babcock pulled Hasek in favor of Osgood during Game 4 and starting with Game 5, the Wings ripped off nine straight wins and eventually went on to win the Stanley Cup in a six-game series against the Penguins.
Osgood was supposed to be No. 1 goalie again for the 2008-09 season, but he struggled so badly that Ty Conklin had to emerge and hold the Wings in the race until Osgood could return to form. Despite finishing with a 3.09 GAA and .887 save percentage -- the worst statistical season of his career -- Osgood was again named the starter when the playoffs began.
He again answered the call, bringing Detroit back to the Stanley Cup Final. This time, the Wings couldn't repeat as Maxime Talbot burned Osgood twice in the second period of Game 7 and Pittsburgh hung on for a 2-1 victory.
Jimmy Howard's emergence the following season dropped Osgood to No. 2 on the depth chart. He stayed there until sports hernia surgery ended his final NHL season three months prematurely.
Follow Dan Rosen on Twitter at: @drosennhl