First half goals from Steve Schumacher and Matt Godden were added to in the second half with a brace for Rowan Liburd as Boro dominated their opponents and were clinical in front of goal.
Darren Sarll's men came out of the blocks flying and were 2-0 up within 18 minutes as Boro caught Southend cold.
After forcing visiting 'keeper Ted Smith into a fine save from a direct free-kick after just five minutes, Steve Schumacher went one better on eight minutes when he curled another set piece over the wall and into the back of the net.
The midfielder then turned provider with a quick free-kick that saw Matt Godden fire a low shot past Smith, as Boro doubled their advantage with 18 minutes on the clock.
The hosts were smelling blood and continued to carve the Blues open at will with some incisive attacking play. Tom Pett curled over, Godden saw a shot blocked, the lively Rowan Liburd also saw an effort blocked and Luke Wilkinson headed just wide as Southend just couldn't cope with wave after wave of Stevenage attacks.
At the other end Chris Day had been a virtual spectator all half, but then made a fine low save to deny sub Jack Bridge from pulling one back for Southend seven minutes before the break.
Luke O'Neill went even closer moments later when his shot beat Day but cannoned down off the bar, onto the post and away, but when that stayed out you sensed it wasn't going to be their night.
Godden saw a fierce shot turned over by Smith five minutes after the break as Boro continued where they'd left off, before Rowan Liburd - who enjoyed his best game in a Boro shirt - coolly finished inside the area for 3-0 with 63 minutes on the clock, for his first competitive Stevenage goal.
Whatever Southend tried in the second half Boro's defence repelled with relative ease, with Nathan Kerr also enjoying an impressive first start for the club at right-back.
Smith turned a low curling effort from sub Henry Cowans aside and Southend missed a couple of late chances to pull one back as the game drew to a close. However the lively Liburd had the last say, heading home from close-range right on 90 minutes to seal an impressive victory.
Stevenage narrowly missed out on qualifying for the knockout stages of the Checkatrade Trophy but can now turn their attention to the visit of Yeovil Town on Saturday. Tickets for this Category B fixture can be purchased at www.borotickets.co.uk.
Stevenage: Day, Kerr, Wilkinson, Franks, Fox (Cowans 61), Gorman, Schumacher (Slater 73), Tonge, Pett, Godden (Kennedy 65), Liburd
Subs not used: Jones, McKirdy, Henry, Wilmot
Southend: Smith, White, Thompson (Sokolik 46), Barrett, O'Neill, Timlin (Wordsworth 61), Cox, Fortune, King, McGlashan, Kyprianou
Subs not used: Bexon, McLaughlin, Bridge, Williams, Matsuzaka
Attendance: 559 (185 away)