Goals after the break from Jack Wilshere and Alexis Sanchez eclipsed Sergio Aguero's first-half opener and appeared to have handed all three points to Arsenal at the Emirates Stadium.
However, centre-back Demichelis crashed home a header with seven minutes remaining to ensure Manuel Pellegrini's side earned a share of the spoils.
The draw casts further doubt over Arsenal's ability to beat the division's other leading clubs, having only registered one victory against top-six teams last term.
There were plenty of positives for the hosts in an enterprising performance, though, not least from Danny Welbeck who almost marked his first appearance since joining from Manchester United on deadline day with a goal when his dinked effort hit the post.
By contrast Frank Lampard was largely anonymous in his City bow and was replaced by former Arsenal man Samir Nasri at half-time to a plethora of boos from the home crowd.
Pellegrini's men showed their attacking instincts to lead at half-time, though, Aguero adding the finish to a brilliant breakaway.
Arsenal moved ahead when Wilshere capped a fine team move before Alexis' perfectly executed volley made it 2-1.
There was time for one last twist, however, as Demichelis met Aleksandar Kolarov's cross, and Nasri almost silenced the boo-boys when he tapped home a rebound from David Silva's shot, but he was denied by the offside flag.
Arsenal started the match brightly, showcasing some incisive football, and Welbeck had his first sight of goal when he swept a Mesut Ozil centre into the side-netting in the 11th minute.
Welbeck then went agonisingly close to opening his Arsenal account just a minute later.
The pacy forward pounced on a loose pass from Silva and bore down on goal before executing a deft chip over Joe Hart, only for his shot to rebound off the inside of the post.
City struggled to gain a foothold in the game's early stages and saw Lampard and Pablo Zabaleta booked in quick succession as their frustration grew.
But the visitors stole the lead after 28 minutes with a textbook counter-attacking goal.
The ball fell to Jesus Navas who raced clear down the right and played a perfectly weighted pass into the area where Aguero got in between the Arsenal centre-backs to sweep home from eight yards.
The away side grew in confidence after taking the lead and Arsenal's defence was torn apart by a fine City move from which Silva saw a close-range shot well saved by Wojciech Szczesny.
City looked comfortable at the start of the second half, but Arsenal drew level shortly after the hour mark.
Alexis and Aaron Ramsey combined well as the Wales international slipped the ball into the path of Wilshere, whose quick feet bamboozled Gael Clichy and his measured finish beat Hart at the near post.
And Arsenal's turnaround was complete in the 74th minute when Vincent Kompany's attempted headed clearance was nodded to the back post by Wilshere and Alexis showed great technique to volley his shot beyond the reach of Hart.
Arsene Wenger saw Mathieu Debuchy forced off with a serious-looking injury in the 81st minute before the Frenchman's day took another turn for the worse as City equalised.
Substitute Kolarov's corner was blocked but from the follow-up cross Demichelis' header found its way home via the post.
There was almost a late twist City twice struck the woodwork before Nasri thought he had got one over his former side with a close-range finish only to be thwarted by an offside call.
