Dostal made 12 saves in the third to help the Ducks reach overtime.
"He basically gave us a point," Silfverberg said.
Anaheim killed four penalties, all in the second period. The Ducks are 17-for-21 on the penalty kill in the past four games.
"It's unfair what we're doing to that kid, taking that many penalties," Ducks forward Troy Terry said of Dostal. "He's stood in there and been kind of the backbone for us, but we've got to stay out of the box."
The Flames lost their previous five games that had gone beyond regulation.
"We stuck with it, we found a way, it was nice to win a game in OT," Andersson said. "It feels like that's been a long time ago, so it was nice to see that one go in and now we head home."
NOTES: Calgary has won its past five games at Anaheim, and nine of 11 after losing 29 straight at Honda Center. ... Dostal is the first Ducks rookie who has made at least 40 saves more than once. ... McTavish scored for the second straight game and has six points (two goals, four assists) in the past five games.