Boro went ahead in the 21st minute when Lawrie Wilson crossed for Peter Vincenti, who turned and fired past Lions keeper David Forde.
The hosts were 2-0 up on the hour when another Wilson cross was met by a fine volley from Peter Winn.
Last season's top scorer Morison pulled one back for Millwall with a header but Kenny Jackett's side could not find an equaliser.







