Paul Burns fired into the top corner to level after 66 minutes but McManus restored Falkirk's lead five minutes later from close range.
Kenny Deuchar added the hosts' third before Queens' Robert Harris was dismissed for handball on the line but Carl Finnigan missed the penalty.
Falkirk: Olejnik, Marr, McLean, Scobbie, Twaddle, McManus (Deuchar 81), Millar (Mitchell 70), O'Brien, Flynn, Finnigan, Compton (Stewart 80). Subs Not Used: Barclay, Higginbotham.
Booked: Compton, Deuchar.
Goals: McManus 15, 71, Deuchar 84.
Queen of South: Hutton, Craig Reid, McKenna (Carmichael 64), Lilley, Harris, Burns, Conroy, McGuffie, McLaren, Holmes, Johnston (Weatherston 74). Subs Not Used: Robinson, Scally, Quinn.
Sent Off: Harris (90). Booked: McKenna, Harris, Lilley.
Goals: Burns 66.
Att: 4,064
Ref: J McKendrick
Source: BBC Sport
Source: BBC Sport