The Flames got off just 21 shots in a meeting of two of the worst teams in the NHL, but Matt Stajan snapped a third-period tie and Calgary won on the road for the 10th time this season.
Berra will join Jonas Hiller of the Anaheim Ducks as one of the goaltenders on the roster for Switzerland when the Olympic hockey tournament begins Wednesday.
Sean Monahan and Dennis Wideman staked Calgary to a 2-0 advantage with second-period goals, but Berra surrendered a score to Thomas Hickey in the final moments of the middle stanza.
Calvin de Haan then tied it for the Islanders 7:31 into the third.
Stajan put the Flames back in front with his 10th goal of the campaign, coming with 5:32 left in regulation, and Mikael Backlund added an empty-netter just before the final horn.
Berra finished with 27 saves while Evgeni Nabokov stopped 18 shots for the Islanders.