Arsenal were punished for a host of missed chances as Manchester City clung on to end a turbulent week with a win.
Barton gave City the lead from the spot
Arsenal's Thierry Henry missed two one-on-ones with City keeper Nicky Weaver and a Robin van Persie shot hit the post before City took the lead.
Justin Hoyte conceded a penalty for a foul on Trevor Sinclair and tireless Joey Barton smashed in the spot-kick.
Ben Thatcher's tackle on Pedro Mendes in midweek had cast a dark cloud over City but they held on valiantly.
The game had got off to a fractious start before settling down with both teams spurning good chances.
Henry was unusually Arsenal's main culprit with the French striker showing his trademark pace and predatory instinct but lacking in his execution.
He was clean through after latching on to Alexander Hleb's lofted ball after 14 minutes only to see keeper Weaver save with his leg.
Arsenal keeper Jens Lehmann gave his side a scare at the other end when his goal-kick struck Bernardo Corradi before rebounding back into his grateful arms.
Barton side-footed agonisingly wide and Corradi saw a header saved low down by a scrambling Lehmann as the home side threatened despite Arsenal's domination.
The visitors have frequently been accused of failing to apply an end product to their play and they showed why as the half wore on.
Henry angled a drive wide, was twice let down by his poor touch in threatening positions and saw another effort saved by Weaver as they strained to break the deadlock.
Van Persie's snapshot beat Weaver but hit the post before Arsenal paid the price for their profligacy.
Thierry Henry was in strangely lacklustre form for Arsenal
A cross-field ball caught out left-back Hoyte, who conceded a penalty for a foul on Sinclair, and Barton dispatched the spot-kick in off the crossbar.
City had the woodwork to thank again when Gunners defender Kolo Toure's header came back off the crossbar, while Van Persie reacted angrily to not being given for a perceived push by Richard Dunne.
The home side could even have extended their lead on the stroke of half-time if Corradi had been more clinical with a poked shot hit straight at Lehmann.
Arsenal continued to pass and probe after the break and Van Persie dragged a shot across goal and wide just after the hour mark as City battled to hold on to their lead.
The home crowd were giving their side plenty of encouragement while Arsenal boss Arsene Wenger threw on teenager Theo Walcott.
Walcott has twice come on to engineer late goals for his side but could not do it again as City got their goal and points tally off the mark to move off the bottom of the table.
Man City boss Stuart Pearce:
"They don't lose many matches and we did it as a collective.
"When you beat Arsenal you have to ride your luck a little bit and I think we did that.
"I think after a tough couple of days one or two people may have doubted us but right through the front to back of the team I'm very proud of them."
Arsenal manager Arsene Wenger:
"We cannot finish what we create at the moment.
"In the last two games we have had a lot of possession but have not made enough out of it through naive mistakes at the back.
"But, there is a lot of potential in the side and when we are completely ready we will win these games."
Man City: Weaver, Richards, Dunne, Distin, Jordan, Sinclair, Barton, Dabo, Vassell (Danny Mills 80), Dickov (Samaras 86), Corradi (Miller 90).
Subs Not Used: Hart, Ireland.
Goals: Barton 41 pen.
Arsenal: Lehmann, Eboue (Flamini 83), Toure, Djourou, Hoyte, Hleb (Adebayor 76), Fabregas, Silva, Rosicky (Walcott 66), Van Persie, Henry.
Subs Not Used: Almunia, Cygan.
Booked: Van Persie.
Ref: U Rennie (S Yorkshire).