With 7:16 remaining in regulation, Ovechkin slid the puck onto the stick of Sheary, who converted the go-ahead goal.
Ovechkin, who had one assist in the first three contests, added some tip-in insurance with 2:58 left to play.
Tyler Seguin, Jani Hakanpaa, Joel Kiviranta and Miro Heiskanen each scored a goal and Mason Marchment added two assists for Dallas.
Anze Kopitar and Adrian Kempe each had a goal and an assist for the Kings, who earned their second win in a row.
Linus Ullmark made 37 saves for his second win of Boston's three this season.