Ryan Hall tested goalkeeper Bobby Olejnik with the first effort of the evening, but his long-range shot was comfortably gathered by the Posh shot-stopper, making his first competitive appearance at London Road.
However, with their first attack of note, Posh got themselves in front as a glorious cross-field pass by Bostwick was helped into the area by Newell to Boyd, he found TOMLIN who made no mistake from close-range with a clinical toe-poke.
After successive corner kicks from the visitors, Posh had a chance to make it 2-0 on 20 minutes as the pace of Paul Taylor got him in behind the Shrimpers back-line, but his low shot was parried by goalkeeper Belford and then cleared by Clohessy.
Lee Frecklington saw a goal-bound effort deflected behind after more good close control from Boyd as Posh continued to threaten. The hosts did make it 2-0 on the half hour mark as Paul TAYLOR picked the ball up just inside the Southend half, skipped past two challenges and fired low past Belford into the bottom corner.
Moments later and it was 3-0 to the rampant Posh as Joe NEWELL scored a sublime chip into the top corner via the underside of the crossbar and Southend were left scratching their heads as to what had gone wrong in such a short space of time.
Five minutes after the re-start, Southend came close to a goal back as Kane Ferdinand's looping header crashed against the crossbar with Zakuani doing well to prevent Eastwood from heading home the rebound. Ferdinand was given time to have another go on the hour mark, but this time his header went wide of the far post.
Posh made sure of their passage into round two on 58 minutes as BOYD finished well on his right-foot after a very clever reverse pass by Lee Tomlin. Hall then struck the crossbar with a sublime free-kick before Darren Ferguson made changes as Danny Swanson and Mark Little were introduced into the fray.
Taylor found the side-netting after bursting into the box on 74 minutes before Grant McCann replaced Frecklington. Taylor shot wide late on after good work from Little as Posh pushed for a fifth goal towards the end.
In stoppage time, substitute McCann saw a free-kick deflected over the top.
Final Score: Posh 4-0 Southend United
Posh: Olejnik, Alcock (sub Little 61min), Brisley, Zakuani, Nthle, Bostwick, Tomlin, Frecklington (sub McCann 74min), Newell (sub Swanson 68min), Boyd, Taylor. Unused subs: Day, Knight-Percival, Ajose, Clarke-Harris.
Southend: Belford, Clohessy, Straker (sub Hurst 66min), Hall, Harris (sub Eastwood 41min), Ferdinand, Phillips, Prosser, Leonard, Barker, Benyon (sub NJie 75min). Unused subs: Bently, Coughlan, Woodyard.
Attendance: 3,225 (370 Southend fans)