Kinkaid, 30, entered the season as the primary backup to Carey Price but struggled in five starts. Kinkaid, who helped lead the New Jersey Devils to the postseason in 2017, was just 1-1-3 for Montreal, with a 4.24 goals-against average.
Cayden Primeau, 20, was recalled from Montreal's American Hockey League affiliate to take Kinkaid's seat behind Price, who stopped 21 shots en route to his 11th win of the season Tuesday.
The Canadiens have back-to-back games on Thursday and Friday, against the Colorado Avalanche and New York Rangers, respectively, with Price likely starting one of them. The schedule will allow Montreal a chance to see Primeau, the No. 199 pick of the 2017 NHL draft out of Northeastern and the son of former NHL forward Keith Primeau, against elite competition.
"That's just the thing," Canadiens coach Claude Julien said. "The next four games, we have two back-to-backs. So, there's no doubt that we're going to get an opportunity to see him.
"We think Primeau has a great future. We're going to see what he brings."
The win over the Islanders put an end to a frustrating 0-5-3 skid for the Canadiens, and helped the club to avoid the first nine-game skid since the 1939-40 season.