The contest had the type of snarl at times unbefitting a September fixture, too, including some general disagreements between the two sides in the scoreless third period.
Klapka delivered a pair of punishing body-checks, while Weegar also laid out Canucks winger Vilmer Alriksson with a heavy hit in the second period.
Dan Vladar and Devin Cooley shared a workmanlike performance in goal; Vladar turned aside 15 of 17 shots over his 40 minutes of work, while Cooley parried away all 10 attempts that landed on goal in period three.
Calgary outshot Vancouver 32-27 overall.
The Flames went 0-5 on the powerplay, while the Canucks finished the night 0-4.
Yegor Sharangovich led all Calgary skaters with four shots on goal.
The Flames won 60% of the face-offs, with Mikael Backlund enjoying 16 wins from his 19 attempts on the night.