Casey DeSmith made 28 saves for the Canucks, who prevailed despite being held to 16 shots on goal.
Drake Batherson and Artem Zub scored for Ottawa, which has dropped six of eight overall and five straight at home.
Just 2:45 later, a Senators' own-zone turnover ended up with Mikheyev going through Forsberg's legs for a 2-0 Vancouver lead.
Batherson took advantage of a Vancouver turnover in its own end, then beat DeSmith for his third goal.
Ottawa, which outshot the Canucks 11-3 in the opening period, tied things with 9:02 left in the second, when Zub's strike was redirected into the net by the stick of Pettersson.
Persons:
Elias Pettersson, Ilya Mikheyev, Pettersson, Casey DeSmith, Ottawa's Brady Tkachuk, Miller, Ottawa netminder Anton Forsberg, Mikheyev, Pettersson's, Drake Batherson, Artem Zub, Forsberg, Brock Boeser's, Batherson, DeSmith, Zub
Organizations:
Vancouver Canucks, Ottawa Senators, Canucks, Ottawa, Senators, Thomson
Locations:
Vancouver