Roberto Mancini's side simply did not look like a side in need of a victory tonight, conceding after just seven minutes when Jason Puncheon slotted home.
Hart could have possibly done better with the shot that led to the opener, but there was no doubting his culpability for Southampton's second.
Excellent team interplay put through Rickie Lambert, whose fierce drive squirmed through the England international's grasp, allowing Steven Davis to bundle home.
Edin Dzeko reduced the deficit as half-time approached, although a two-goal lead could have been restored on the stroke of half-time had referee Martin Atkinson not waved away Jay Rodriguez's penalty appeals.
That was soon forgotten, though, as Barry passed into his own goal unchallenged to put Saints on course for a first win since Pochettino replaced Nigel Adkins at the helm.
On the opening day of the season the newly-promoted side were valiant in a 3-2 defeat at the Etihad Stadium.
It was a similarly end-to-end encounter this evening, with Saints dominating the proceedings early on and netting a seventh-minute opener.
After Barry was dispossessed, Puncheon burst down the right flank and played through the unmarked Rodriguez. Hart managed to deny the winger but the ball fell kindly for Puncheon, who slotted home calmly in front of the Northam End.
City were struggling to deal with Southampton's attacking intent in an opening 15 minutes in which a tame Sergio Aguero effort was all they had to show for their efforts.
They eventually began to settle but were soon rocked by a second Southampton goal in the 22nd minute.
Lambert collected the ball on the right and played a neat one-two with Puncheon, before cutting back and firing a shot that Hart let slip through from his midriff, allowing Davis to poke home.
Saints fans ironically bellowed 'England No.1' after the gaffe, before directing their attention at referee Atkinson.
First they took umbrage with his decision to book Lambert for hauling back Joleon Lescott, before he then awarded a foul on the edge of the box after Dzeko took a tumble.
Rodriguez saw a right-foot effort go just inches wide of Hart's far post as the home side pressed for a third, with Nathaniel Clyne seeing a strike deflect behind.
Pablo Zabaleta floated ball to the back post just evaded Aguero as City looked for a goal, which came six minutes before half-time.
The Bosnian striker got himself in the way of terrible Saints corner, before bursting up the field and tucking home a Zabaleta cross.
It was harsh on the hosts, who felt hard done by in stoppage-time when Rodriguez was brought to ground in the area by Yaya Toure, captaining the side on his return from the African Nations Cup.
Atkinson awarded a corner instead of a spot-kick much to the home fans' frustrations - but they were celebrating soon after the restart.
After Puncheon hammered over moments into the second half, the winger could then not quite latch onto a Lambert pullback, which Barry inexplicably passed into his own goal.
Gael Clichy was booked soon after as City's frustrations became evident, with Saints pushing for a fourth.
The visitors were having to defend with all they had and hope for a chance on the counter, with Artur Boruc reacting well to palm away an Aguero strike wide when they did voyage forward.
James Milner, on moments earlier for Samir Nasri, shot wide from the resulting corner but City were soon back on the defence.
Toure was booked for a foul on substitute Adam Lallana soon after, before Fox limped off to be replaced by Frazer Richardson.
Aleksandar Kolarov and Maicon were City's final introductions, with the latter soon denied from close range by Boruc.
James Ward-Prowse replaced Davis for what a nervy final 10 minutes in which City were kept at bay, meaning United could go 12 points clear at the top should they beat Everton tomorrow.
Source: Manchester City MAD