Chiasson was playing in the 16th game of his NHL career and this was the third time he has scored twice in the same contest.
He delivered the only goal of the first period and then gave Dallas the lead for good at 2-1 midway through the second.
The second score for Chiasson touched off a three-goal Dallas outburst in the span of 1:01 with Jamie Benn and Brenden Dillon accounting for the other tallies. Benn tacked on a second goal early in the third.
Lehtonen has the third best save percentage and the fourth best goals-against average in the NHL, but he missed five games with a lower body injury suffered on Oct. 11 against Winnipeg.
Lehtonen stopped 28-of-29 shots to help end a two-game Dallas skid.
Karri Ramo gave up all five goals on 34 shots. Calgary has lost two in a row and four out of five.
Swim Week Miami Beach 2014 [PHOTOS]