Cameron Gardner and a Michael Bostwick own goal had put the Mariners in command at the break.
However, substitute Oliver Wilson reduced the arrears in the first minute of the second half, before Mooney struck on 60 and 75 minutes.
Boston (4-1-2-1-2): Cameron Gregory; Zak Mills, Michael Bostwick, Tom Leak, Brad Nicholson; Jordan Richards; Tom Edge (Martin Woods 59), Keziah Martin; Sam McLintock (Keaton Ward 59); Jimmy Knowles (Kelsey Mooney 46); Michael Gyasi (Oliver Wilson 46). Subs (not used): Dylan Hill, Sam Essien, Will Hall, Tyler Knowles, Jake Lovelace (gk).
Referee: Josh Smith.
Attendance: 891 (218 visitors).
PIC: Russell Dossett.