The result leaves Roberto Mancini's side eight points behind leaders Manchester United with only six league games remaining after Sir Alex Ferguson's side enjoyed a comfortable 2-0 win over 10-man Queens Park Rangers at Old Trafford earlier in the day.
In truth, City can have few complaints about this result with former Internazionale forward Balotelli fortunate to remain on the park for 89 minutes after careering into a number of poorly-timed tackles throughout the afternoon.
Referee Martin Atkinson somehow missed Balotelli's wretched knee-high tackle on Alex Song with his studs showing that should have produced a straight red card on 19 minutes.
He was predictably booked for a late tackle on Bacary Sagna before half-time, but did not curb his enthusiasm. Balotelli continued to show flashes of dissent before another desperate tackle on Sagna approaching injury time prompted Atkinson to finally produce the red card.
Arteta won it for an impressive Arsenal side when he bounded onto a loose ball to send the ball flying beyond the despairing dive of England goalkeeper Joe Hart on 86 minutes from 25 yards out, but there is little doubt that Balotelli made as much an impression on the afternoon's happenings.
Balotelli has received four red cards since joining Manchester City - three in the Premier League and one in the Europa League.
His red card contributes to a day of woe for City who are on a three-match winless run in the Premier League for the first time under Mancini, a manager fuming with Balotelli as he trotted slowly off the park having been sent off.
More importantly, City's hopes of a first English title since 1968 appear to be over for another season after this outcome.
Hart, Vincent Kompany and Joleon Lescott were outstanding for City in defence as Arsenal threatened to rip them to shreds, especially in the opening 25 minutes.
City's best moment of the match came when Sergio Aguero forced Wojciech Szczesny to swipe the ball over his bar early in the second period, but even Aguero was a poor imitation of his early season self as he departed to be replaced by Carlos Tevez in the closing 10 minutes.
Their day began to unravel when they lost Yaya Toure to injury in the opening minutes of the match. He had been booked for hauling back Tomas Rosicky on two minutes before limping off.
Van Persie saw a header fly against the back of Thomas Vermaelen on 15 minutes that was destined to find the net while the Dutch forward also nodded against a post from Song's pass on 61 minutes.
With Arsenal in the ascendancy - this win leaves them two points ahead of Tottenham in third spot - Walcott saw a shot come off a post on 75 minutes before Vermaelen slipped trying to score from the rebound with Yossi Benayoun also failing to steer it into the net.
It looked like City might escape with a draw, but they were barely worth a point from a typically frantic afternoon in which their championship hopes surely ended.