Florida opened the scoring 11:45 into the first period on a power play. Ruslan Salei's shot from the blue line was stopped, but Olli Jokinen was right there to jam in the rebound.
That was the only goal until the third period when Richard Zednik scored off a lucky rebound at 7:38. Florida rookie defenseman Cory Murphy rounded out the scoring at 17:42.
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 a fine performance by Calgary goaltender Matt Keetley, who was pressed into service when expected starter Curtis McElhinney took a shot in the groin during pregame warmups.
Keetley responded by making 31 saves, many of them sensational. The most impressive stretch was consecutive breakaway stops seconds apart in the second period while Florida was short-handed.
It was a rough debut for Calgary's power play, which went 0-for-11 and yielded a short-handed goal.
For their first exhibition game, the Flames dressed a large number of veteran players. Among them was a forward line of Alex Tanguay, Matthew Lombardi, and 35-year-old Owen Nolan, who signed a one-year deal with Calgary in July.
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Olli Jokinen (power play) Assist: Ruslan Salei, Cory Murphy