Freddie Ljungberg headed a 75th-minute equaliser but the real winners were title favourites Chelsea, who now lead the Gunners by seven points after beating Middlesbrough.
The result showed up the lack of depth in injury-hit Arsenal's squad. They have the smallest squad of any of the top three and their much-changed team lacked fluency though their effort stretched City to the limit in the dying minutes.
City's defence is much tighter and more disciplined this season and Richard Dunne was the cornerstone of their resistance while Wright-Phillips' pace and control always provided them with an outlet to relieve the pressure.
It was the youngest Premiership side that Arsene Wenger had fielded in more than eight years as Arsenal boss. Nineteen-year-old Swiss centre-back Philippe Senderos made his Premiership debut in place of ankle victim Sol Campbell while 20-year-old right back Justin Hoyte continued to deputise for Lauren.
Seventeen year-old Cesc Fabregas lined up again alongside Patrick Vieira in central midfield, in the continued absence of Gilberto and Edu. Robin van Persie partnered Thierry Henry because Dennis Bergkamp and Jose Antonio Reyes are still sidelined.
Robbie Fowler tested the Gunners defence with a header in the opening minute, finding space on the right to force a good save from Manuel Almunia.
Henry roused the Gunners. He whipped over a low centre but Arsenal lacked bodies in the box as the ball flashed across goal.
Henry threatened again with a 25-yard free-kick that Robert Pires missed by inches. Hoyte then surged forward after winning a tackle but finished with a weak shot that was held by David James.
Henry set up a 19th-minute chance for Van Persie who shot weakly at James from 15 yards. Ashley Cole was then robbed by a swift challenge after a neat combination with Pires while Dunne halted Henry with a recovery tackle, before the Premiership's top scorer fired a volley wide.
But it was Wright-Phillips who struck in the 31st minute, lashing in a trademark 25-yard shot after Vieira had lost the ball on the edge of the Gunners' box. Wright-Phillips' stepfather, Arsenal's all-time top scorer Ian Wright, could hardly have managed a more impressive finish.
City pulled bodies back to defend their lead. James held Henry's curled free-kick two minutes later and Vieira headed wide with James stranded at a Pires corner before Van Persie shot wide again
Sylvain Distin prodded a low shot past his own goal as the Gunners piled forward at the start of the second half before James parried away Cole's close-range header.
But Arsenal were lucky to escape when Almunia scuffed his clearance from Hoyte's back pass and Jon Macken failed to capitalise.
James was then forced to tip Pires' 70th-minute volley onto the bar and away to safety as the desperate Gunners stoked up the pressure.
City finally cracked five minutes later, when Henry's acrobatic overhead kick found Ljungberg who headed past James.
City rode their luck in the closing stages. Van Persie cracked a 78th-minute free kick against the junction of post and bar and then volleyed over the bar from substitute Jermaine Pennant's cross.
Pires then picked out Henry who headed over with time ticking away. It was Arsenal's last chance and Wenger looked a very frustrated manager at the final whistle.
City have still not beaten Arsenal in 12 Premiership matches but they will take most satisfaction from this draw.