Barrett and Hunt seal Blues' first win of the season against the Posh.
Noel Hunt scored his first goal at Roots Hall, as Southend United picked up their first win of the League One season.
Blues boss Phil Brown made just one change from the side that picked up a point at Coventry City, with Anthony Wordsworth replacing Will Atkinson in the starting XI.
Southend United started the first half as the stronger side, but had to be alert to clear their lines in the 12th minute, when an in-swinging corner from Jon Taylor forced Michael Timlin to clear off the goal-line.
Blues immediately countered, with David Mooney heading over at the far post, following an inviting ball in from John White.
Mooney threatened again moments later, when he latched on to Ben Coker’s ball forward before drawing a save from Peterborough goalkeeper Ben Alnwick.
The chances kept falling for Mooney, after a deep ball in from White presented the forward with an opportunity for a headed effort, but it failed to trouble Alnwick.
Taylor charged forward down the right flank before firing a low effort into the side-netting, as Posh made a rare attempt at troubling the Blues defence.
Noel Hunt then put the ball across the face of goal, but despite a sliding attempt for the ball, Wordsworth was unable to get the telling touch.
Blues went in front in the 33rd minute, when Adam Barrett pounced to poke home after Hunt’s initial effort was parried by Alnwick.
David Worrall then lifted a ball towards the far post, that culminated in Ryan Leonard volleying over on his left foot after a knock-down from Mooney.
Marcus Maddison drifted from the right wing with one minute of the first half remaining, before seeing his curling left-footed effort palmed away by Dan Bentley.
Conor Washington was replaced by Jack Collison during the interval, as Peterborough boss Dave Robertson made his first change.
The first chance of note in the second half fell the way of Peterborough, with Michael Bostwick’s thumping effort deflecting off of a Blues player before it cannoned back off of the crossbar.
Hunt was then presented with an effort to double the lead for Blues, after Mooney unlocked the Posh defence with a smart through ball. However, the Irishman was denied his first goal at Roots Hall by the legs of Peterborough keeper Alnwick.
Peterborough substitute Collison then curled an effort at goal that left Blues thankful for a headed clearance from Coker, with the ball destined for the back of the net.
Hunt was thwarted once again just moments later, after his headed effort was turned away by Alnwick, before his defence eventually scrambled the ball clear of danger.
Peterborough’s second change followed swiftly after, with Souleymane Coulilbaly replacing Joe Gormley.
Wordsworth then fired just over with a volley from just outside the penalty area.
Blues eventually doubled their advantage in the 70th minute, when Hunt rose to head home from a free-kick that was lifted in by Coker. The free-kick was awarded after a foul by Bostwick which saw the Peterborough midfielder pick up a yellow card.
Hunt was involved again six minutes later, lifting a ball onto the head of Mooney, only for the former Leyton Orient man to head wide of goal.
Leonard then burrowed into the penalty area from the byline, before seeing his cut-back squandered by Hunt, who couldn't get the ball out from under his feet.
Hunt went close once again in the 82nd minute, after a smart reverse pass from Mooney allowed the former Reading forward to swivel and flash an effort across the face of goal.
Peterborough made their third change in the 83rd minute, when Kyle Vassell came on to replace Alex Davey.
Worrall then raced away from his man before crossing for Mooney at the far post, but his headed effort looped just over the far post.
Blues boss Brown chose to withdraw goalscorer Hunt in the 85th minute, as Joe Pigott entered the fray for Blues.
Timlin cut the ball back for Pigott, who could only fire wide almost immediately after his arrival.
The second change for Southend followed within three minutes, as Stephen McLaughlin replaced Worrall.
Maddison then pulled one back for the visitors in the 90th minute, stroking the ball past Bentley after Coker’s attempted block.
Luke O’Neill then replaced Mooney as Blues made their final change of the afternoon.
Maddison then curled an effort over the Southend goal as Peterborough pushed for a late equaliser.
Posh keeper Alnwick went up for a corner in the 94th minute, which Blues cleared in what proved to be the final action of the game.
SOUTHEND UNITED: Bentley; White, Rea, Barrett, Coker; Leonard, Wordsworth, Timlin, Worrall (McLaughlin - 87’); Mooney (O’Neill - 90’), Hunt (Pigott - 85’).
Unused Substitutes: P. Smith, Prosser, Deegan, Payne.