Detroit advanced in the playoffs for just the second time since 2002.
The win also gave the Red Wings a much-needed break after beating the Flames twice in less than 36 hours in arenas nearly 2,000 miles apart.
"Some guys are new to the team, so I'm sure they're happy," star defenceman Nicklas Lidstrom said Monday when the team arrived home. "For some of us that have been here for a while, it's a relief to win in the first round."
The Western Conference's top-seeded team won the series 4-2 over Calgary and will be able to rest before hosting San Jose or Dallas in Game 1 on Thursday.
If the sixth-seeded Stars eliminate Vancouver on Monday night, they will play Detroit. If not, the fifth-seeded Sharks will match up with the Red Wings.
"In the Western Conference, seeds don't mean anything," forward Kris Draper said.
Entering the playoffs, the Red Wings were determined to avoid the early exits that have haunted them recently. And they were confident in the changes made to help.
Detroit brought back goaltender Dominik Hasek to replace Manny Legace.
The Red Wings added depth, toughness and speed with acquisitions. They also gave younger players a chance to play after losing Steve Yzerman to retirement and Brendan Shanahan to free agency last summer.
Most importantly perhaps, Red Wings coach Mike Babcock insists the current team is not carrying around "baggage" from previous playoff flops.
"This team isn't about '03, '04 or '06," Babcock said.
Detroit tied Buffalo for the most points in the NHL - losing a tiebreaker for the Presidents' Trophy a year after winning it - and has at least tied for the most points in the league in three straight seasons and four of five.
But regular-season success hasn't carried over into the playoffs much recently for the storied franchise.
Since winning back-to-back Stanley Cup titles in 1997-98, Detroit lost in the first round in two of the previous three post-seasons and only made it past the second round in 2002, when it won a 10th championship.
Of course, just surviving the first round this year isn't going to satisfy fans.
Babcock said that won't change his players' mind-set.
"I don't think you'll see us carrying the weight of the world around," he said. "We're just going to go out and play."
The Red Wings didn't want to play against Calgary on Tuesday night at home in Game 7 and Franzen granted their wish by ending the series.
"It will be very nice to get the break because we played back to back with travel," said Robert Lang, who tied Game 6 with a goal late in the second period.
Franzen's series-winning shot turned the Saddledome eerily silent - besides the Red Wings shouts of joy.
"It was a great relief to see Johan score that goal. Everybody's ready to go," Hasek said in Calgary after the game.
The Red Wings scheduled a "very optional" skate on Tuesday and didn't expect more than a handful of players to show up for it. All of the healthy players will practice on Wednesday, when they will begin to prepare for their second-round opponent.
Forward Tomas Holmstrom is day-to-day with an eye injury after Calgary's Craig Conroy hit him with his stick at 6:44 of overtime Sunday night. Defenceman Brett Lebda is day-to-day with a concussion and ankle injury. The team expects to know Thursday whether Lebda will be available for Game 1.