Jason Roberts bundled home the second from close range and McCarthy turned in a third before half-time.
Rovers took an early lead when Jason Roberts tucked away Brett Emerton's right-wing cross from close range.
Having fallen behind to Jason Roberts' opener, Martinez was delighted with the manner in which his team responded.
Blackburn's Carlos Villanueva clipped the bar in the first half before Jason Roberts missed a free header close in.
Jason Roberts was making The Polar Bear Family and Me, in which bears were filmed from a clear plastic hide.
"I'm OK now - I think we've only Jason Roberts, " said Allardyce.
Allardyce desperately needed a change in momentum and introduced striker Jason Roberts for Nikola Kalinic - a decision not popular with the local fans.
Blackburn defeated Wolverhampton Wanderers 3-1 with El-Hadji Diouf, Jason Roberts and David Dunn scoring before Stefan Maierhofer scored a late consolation for the promoted visitors.
Rovers struggled to create a clear-cut chance and were denied two penalties when Gareth Barry held Benni McCarthy and Zat Knight tugged at Jason Roberts.
Jason Roberts is being honored as a Champion of Change for his time and effort developing innovative ways to help grow and expand the transportation industry.
Blackburn continued to look the more composed side, and it took a vital interception from Joseph Yobo to deny Jason Roberts after he weaved his way into the area.
Andre Ooijer, Stephen Warnock, Keith Andrews, Jason Roberts and Pedersen also returned to the side, while Sunderland manager Roy Keane settled for bringing in Teemu Tainio to replace Jordan Henderson in midfield.
With just five minutes gone Roberts had crossed for the first try, as Jason Spice took a quick tap penalty and fed Jamie Robinson.
Jamie Roberts, Leigh Halfpenny, Dan Evans, Martyn Thomas and Jason Tovey are other potential candidates, with Morgan Stoddart still injured.
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