It was the fourth shutout of the season for Quick, who faced 15 shots in the second period and just two in the third.
Dustin Brown scored a goal early in the first period and then assisted on Dwight King's insurance goal at 3:30 of the third period.
The win was the third in a row for Los Angeles. Calgary had lost two-of-three heading into the Olympics hiatus.
Joni Ortio faced 24 shots for the Flames, who went 0-for-4 on the power play.