D'Agostini, who opened the scoring 6:53 in, jumped on a loose puck in front of the Islanders' net and put a quick shot past Mike Morrison after Montreal blew its second one-goal lead with 5:57 remaining in the third.
Islanders defenseman Radek Martinek tied it at 2 when he scored 14:03 into the third. Jeff Tambellini also scored to draw New York even in the second.
Guillaume Latendresse had a goal and an assist and highly touted Canadiens prospect Carey Price made 22 saves.
Latendresse, who scored 16 goals last season as a 19-year-old rookie, finished off Tomas Plekanec's centering pass 14:27 into the second. He also set up D'Agostini's first-period goal.
Price, drafted fifth overall by Montreal in 2005, played the entire game in his bid to open the season on the Canadiens' roster.
The 6-foot-3 native of Vancouver led the Canadian national junior team to a gold medal last season before joining Hamilton -- Montreal's AHL affiliate -- and leading the Bulldogs to the Calder Cup with an MVP playoff performance.
Price allowed three goals on 17 shots Tuesday after he replaced Jaroslav Halak midway through a 5-2 loss to Pittsburgh.
Canadiens No. 1 goalie Cristobal Huet will start Saturday night against Ottawa. Halak, scheduled to face Boston on Sunday in Halifax, is widely expected to begin the season as Huet's backup after a strong showing as a rookie at the end of last season.
Wade Dubielewicz stopped nine of 10 shots made before he was replaced 8:44 into the second by Morrison, who also made nine saves.