The Austrian stopper kept out Sam Hoskins' 90th-minute spot-kick - the last of a string of saves that helped protect the slender lead gained after Jordan Richardson had fired home midway through the first half.
The result and performance illustrated the strong character of the team as they notched their maiden points after a season of struggle up to now.
Southampton, meanwhile, will be frustrated at the outcome of a game they largely were on top of and in which they created the best opportunities.
They will be glad to see the back of the Potters after their Under-18s also lost their unbeaten record at Clayton Wood Training Ground on Saturday - Ryan O'Reilly, who netted for City in that game, was called up for today's encounter on the south coast.
He slotted into central defence alongside Jordan Keane, while Jadan Hall was given a starting berth in the five-man midfield.
Keen to make amends for their 7-2 defeat at Tottenham Hotspur, Stoke were fast starters and could have gone ahead after just five minutes - Richardson cleverly found Ben Glasgow charging down the right, and his low cross was met by George Rigg, but his effort was parried by Artur Boruc.
Corby Moore had the hosts' first sight of goal a quarter of an hour in when he drilled wide from 25 yards, but Stoke were very much the equal of their unbeaten opponents.
They got a reward for their endeavours by breaking the deadlock on 26 minutes.
James Campbell picked out Richardson with a precise pass, and the attacking midfielder played a one-two with Hall before turning and firing a sweet shot past Boruc into the left-hand corner.
Forced into action, Southampton utilised the trickery of Steve de Ridder on the left-wing, and he forced a smart save from Bachmann after a powerful curling shot.
Bevis Mugabi went close with a header on 37 minutes, but Stoke were generally effective in snuffing out any threat in their defensive third and got to half-time with their one-goal lead intact.
Determined not to disappoint the watching Nigel Adkins, Southampton were the quicker to settle after the break, with Mugabi and Hoskins missing the target when presented with decent openings.
City 'keeper Bachmann then made two outstanding stops in the space of a minute - initially from a Luke Shaw effort that looked destined for the net, and then from a Jordan Turnbull header from the subsequent corner.
Ben Reeves' free-kick stung his hands once more, but Saints were getting irked by their lack of efficiency in front of goal.
At the other end, Richardson's deflected drive forced Boruc into action, while de Ridder should have done more than clear the bar when he found space in the Potters' area.
Stoke remained disciplined out of possession, but victory almost slipped through their fingers in stoppage time - Keane was adjudged to have handballed Reeves' cross, but Bachmann palmed Hoskins' penalty away.
It proved to be decisive, as even though Southampton continued to press, their efforts proved futile and it was City who took the points.
Coach Dave Kevan said afterwards: "We want them to enjoy this, because they've had a tough baptism of fire in this league.
"We got a goal and it gave us something to hang onto. Obviously Southampton dominated possession, but we were very disciplined and kept our shape well. I'm very pleased for the boys."
Stoke City: Bachmann; Glasgow, Keane, O'Reilly, Campbell; Hall (Richards 73), Richardson, Clarkson, Rigg, Musungu; Trialist (Alabi 33 (Rossi 81)). Subs not used: Eve, Coulson.
Southampton: Boruc; Young, Mugabi, Turnbull, Shaw; Sinclair (Seidi 61), Moore, Robinson, Reeves, de Ridder (Rowe 83); Hoskins. Subs not used: McCarthy, Johns, Curtis.