Florida opened the scoring 11:45 into the first period on a power-play when Ruslan Salei's shot from the blue-line was stopped but Olli Jokinen was right there to jam in the rebound.
That would turn out to be the only goal until the third period when Richard Zednik scored in Florida's second goal on a lucky rebound at 7:38.
Rookie defenceman Cory Murphy rounded out the scoring at 17:42 of the third.
Vokoun, acquired in the summer from Nashville, made 10 saves before giving way to Anderson halfway through the second period. Anderson made 17 stops.
The loss spoiled an inspired effort by Calgary goaltender Matt Keetley, who was pressed into service when expected starter Curtis McElhinney took a shot in the groin during the pre-game warm-up.
Keetley responded by making 31 saves, many of them sensational stops. The most impressive stretch was consecutive breakaway stops just seconds apart in the second period while Florida was short-handed.
Keetley, drafted by the Flames in the fifth round of the 2005 draft, played his junior hockey with the Medicine Hat Tigers. Last season he was named the Western Hockey League playoff MVP and then won the Hap Emms Memorial Trophy for most outstanding goaltender at the Memorial Cup.
There is an open job to back up goaltender Miikka Kiprusoff and originally it was expected to be a battle between McElhinney and Brent Krahn. However, Keetley may have added himself into the mix.
It was a rough debut for Calgary's power-play, which went 0-for-11 in addition to giving up a short-handed goal.
For its first exhibition game, Calgary dressed an unusually large number of veterans. Among them was a forward line of Alex Tanguay, Matthew Lombardi, and 35-year-old free agent signing Owen Nolan, who inked a one-year deal with the Flames in July.
Lombardi and Tanguay turned a couple of nice passing plays into dangerous scoring chances early in the game while Nolan looked solid.
Notes: After his goal, Zednik slid into the end boards heavily and ended up leaving the ice gingerly, looking to be favouring his shoulder... Brett Sutter, son of Flames general manager Darryl Sutter, played left-wing on a line with Dustin Boyd and David Moss. . . . Also making his Flames debut was D Adrian Aucoin, who was paired with Robyn Regehr. Aucoin, 33, was acquired from Chicago in a trade that sent Andrei Zyuzin to the Blackhawks. . . . The Flames and Panthers meet again on Tuesday night in Saskatoon.