Iginla gave the Flames a 2-0 lead in the first period and scored again early in the third to make it 4-2.
Martin Kiprusoff had 38 saves, including 19 in a busy second period in which Matt Stajan scored Toronto's second goal of the game.
Francois Beauchemin scored the Leaf's other goal in the first period. Jonas Gustavsson and Vesa Toskala split time in the Toronto goal and faced a total of 22 shots.
The Flames took a quick 2-0 lead in the first period on Ingila's slap shot at 1:21 and Nystrom's tip-in off Boyd's shot 16 seconds later.
Boyd boosted Calgary's lead back to two goals later in the period after Beauchemin had scored on the power play at 5:24.