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Matt Lawlor's side, ranked 84 places below the Gunners in the football pyramid, took the lead through Aaron Loupalo-Bi in the 21st minute.
Viktor Gyokeres pulled the visitors level after the break, but Mikel Arteta's squad, who beat Town in the previous round, couldn't find a winner and were reduced to 10 men in the 86th minute, when teenager Max Dowman kicked out following a challenge by Harrison Neal.
Arsenal's Max Dowman reacts after being shown a red card during the Carabao Cup clash. (Image: PA)
Davies came on as a 82nd sub for the Lancashire sub, before converting one of the spot kicks in the 5-3 penalty win at Highbury Stadium.
The 27-year-old spent time in the academy at Ipswich before being released at 16, and began his senior career with Coplestonians in the Suffolk & Ipswich League.
He moved on to Leiston in the Southern League Premier Division Central, scoring 50 goals over two seasons. That led to a move to Braintree Town, where he netted seven times in 14 National League South games.
Will Davies, pictured during his spell at Leiston. (Image: Ben Cunningham)
His form at Cressing Road soon drew the attention of York, who secured his services in November 2023, before he moved to Sutton United following a loan spell at Bromley.
In the summer of 2025, Davies stepped up to the EFL for the first time, signing for Fleetwood for a transfer fee reported to be one of the largest ever received by Sutton.
He has since become a regular for the Cod Army, who will find out their quarter-final opponents when the draw takes place following Chelsea's game against Liverpool this evening.