Three goals in six first-half minutes from Joe Anyinsah, Mustapha Carayol and Danny Woodards put the League Two side in control, before Byron Anthony’s flying header made it four at the Testwood Stadium.
Nathaniel Sherborne did pull a goal back with 20 minutes left but it proved to be little more than a consolation as substitute Eliot Richards struck twice, with Ben Swallow sent off for a two-footed lunge.
After hammering Bradford Park Avenue in round one, the Evo-Stik Southern Premier side were eyeing a money-spinning third-round tie, but following a dominant six-minute first-half spell it was the Pirates who went through. First it was Anyinsah, who slalomed past Michael Gosney before crashing the ball beyond Grant Porter, and then Carayol smashed home just two minutes later.
Defender Woodards struck a sweetly-timed third and after the break Anthony’s flying header extinguished any hope of a Totton comeback. Sherborne’s flicked header salvaged a deserved consolation for the hosts, but Richards’ rising drive and then calm stoppage-time finish completed the rout.
Swallow’s late dismissal took little of the gloss off the win, as Rovers secured their place in the third round.