The result leaves City in fourth place - 11 points behind leaders Chelsea - while Arsenal remain behind Manchester United in sixth place, and are currently seven points off a Champions League spot.
Given the recent speculation regarding his future, Arsene Wenger would have hoped for a fast start from his side but they fell behind as early as the fifth minute.
It was almost 2-0 when De Bruyne struck a shot against the post from 20 yards, before David Silva was denied by Ospina after collecting the rebound.
Arsenal slowly found their feet and should have equalised through Mesut Ozil, who scuffed a shot straight at Wilfredo Caballero from close range, while Nacho Monreal blazed over from the edge of the penalty area.
However, the Gunners eventually got on level terms through Walcott, who capitalised on remaining onside thanks to Gael Clichy by poking home from 12 yards.
Parity was only restored for two minutes, though, as Aguero regained the lead for the visitors with a low shot into the bottom corner from an acute angle after being teed up by Silva.
City went looking for a third at the start of the second half and Aguero probably should have found it after meeting a Jesus Navas cross, but he sent his header wide at the near post.
A minute later, Arsenal were level. An outswinging corner from Ozil found Shkodran Mustafi, who directed a fine header into the far corner of Caballero's net after jumping ahead of Danny Welbeck.
While the home side were looking to build on their second goal, it was City who were creating the opportunities, with Fernandinho's volley from the edge of the box being punched away by Ospina.
Midway through the second half, Aguero had a chance to direct a header into the far corner from close range but he put it too close to the goalkeeper.
Wenger made the call to introduce Olivier Giroud for Walcott, but it did not work for the Frenchman and it was City who looked the more likely as the game entered the closing stages.
With five minutes left, Silva was presented with an opening from 20 yards, but he failed to make a proper connection with his left-footed drive.
City felt as though they should have had a penalty in added-on time when Monreal appeared to handle inside the area, but their appeals were waved away as Wenger's side claimed a point which they probably deserved. body check tags ::