Izale McLeod's double ended Farsley Celtic's FA Cup hopes and took MK Dons through to the FA Cup second round.
McLeod volleyed the Dons in front from Gareth Edds' pass and he added his second from the penalty spot after Roy Stamer tripped Paul Mitchell.
Conference North Farsley then had Bambrook sent off for a cynical foul on Scott Taylor and Stamer also saw red for a second yellow card late on.
Bambrook had Celtic's best chance but his shot was saved by Adolfo Baines.
Milton Keynes Dons: Baines, Jamie Smith, Crooks, Diallo, Lewington, Edds, Mitchell, Andrews (Taylor 63), McGovern, McLeod (Rizzo 82), Platt (Hastings 85).
Subs Not Used: Bankole, Page.
Goals: McLeod 63, 76 pen.
Farsley Celtic: Cuss, Stabb, Crossley, Serrant, Pemberton (Nestor 72), Watson (Midgley 24), Bambrook, Knowles, Stamer, Grant, Reeves (Walls 56).
Subs Not Used: Morgan, Thackray.
Sent Off: Bambrook (80), Stamer (87).
Booked: Knowles, Stamer.
Ref: M Thorpe (Suffolk).