Barton, who was named in the starting line-up despite his recent actions, was involved in an unsavoury second-half incident that resulted in Arsenal winger Gervinho receiving a straight red card.
Gervinho, who turned down a move to Newcastle to join the Gunners, aimed a punch at Barton after the Newcastle midfielder hauled him from the floor and accused him of diving.
Barton was booked for his actions, but Newcastle were unable to take advantage of their extra man in the closing stages to force a win.
Indeed, it was Steven Taylor and Fabricio Coloccini who caught the eye at the back as they successfully neutered an Arsenal side that scored four goals in the opening 45 minutes on Tyneside last season.
There was no chance of a repeat, with the Gunners failing to force Tim Krul into a single save before the break.
Laurent Koscielny beat the Newcastle goalkeeper to Tomas Rosicky's 31st-minute corner, but Danny Simpson hacked the ball off the line without too much cause for alarm.
The Magpies' first-half attacking proved equally ineffective, with their only opportunity of note seeing Jonas Gutierrez volley well wide following a cross from Danny Simpson.
Pardew swapped Ba with fellow debutant Gabriel Obertan at the break, and the Frenchman added a bit of energy in attack without ever really looking like scoring.
Krul was finally tested when he saved Theo Walcott's low effort in the 64th minute, and the game finally exploded into life when Gervinho was dismissed for aiming a punch at Barton with quarter-of-an-hour left.
NEWCASTLE (4-4-2): Krul; Simpson, S Taylor, Coloccini, R Taylor; Barton, Tiote, Cabaye (Lovenkrands 81), Gutierrez; Ba (Obertan 46), Shola Ameobi (Best 73).
(not used): Forster (gk), Williamson, Gosling, Sammy Ameobi.
ARSENAL (4-1-4-1): Szcesny; Sagna, Vermaelen, Koscielny, Gibbs; Song; Gervinho, Ramsey (Djourou 90), Rosicky (Frimpong 85), Arshavin (Walcott 61); van Persie.
Subs (not used): Fabianski (gk), Jenkinson, Chamberlain, Chamakh.