The Black Cats are in the last 32 with Rochdale, who dedicated their first goal against Hartlepool to terminally ill youngster Joshua McCormack.
Morecambe, Oldham, Yeovil and Coventry also progressed from the group stage.
Marcus Bignot lost his first game in charge of Grimsby, who were beaten 4-2 by Sheffield United in a dead rubber.
League One side Rochdale named five-year-old Joshua McCormack on the bench for their 2-1 win at Hartlepool.
The youngster was diagnosed with a brain tumour last year and was told it was terminal in September.
Following Reuben Noble-Lazarus' opening goal in their 2-1 win, Dale players ran over to the bench to get a shirt with 'McCormack 55' printed on it and held it aloft to show their support.
Sunderland would have been eliminated had they lost to League Two County, and the Premier League club's youngsters trailed with eight minutes left at the Stadium of Light.
However, Josh Maja slotted home to equalise and then Seb Larsson's cross was deflected into his own net by Magpies defender Hayden Hollis.
On the final matchday of the group stages, Sunderland became the eighth development squad to reach the last 32.
Of the 16 category one academy sides invited by the English Football League to enter the revamped competition, three won their group to guarantee a home tie in the second round.
The new-look competition has seen low attendances at many clubs, and only one of Wednesday's eight matches recorded a four-figure crowd.
Carlisle, who had already qualified from their group, drew 1,420 to Brunton Park as they beat Fleetwood 4-2, but only 380 fans watched Rochdale's win over Hartlepool.
Elsewhere, Romanian defender Florin Gardos played a competitive 90 minutes for the first time since February 2015 as Southampton's development squad beat Crawley Town 4-0.
The 28-year-old defender has been sidelined with a long-term knee injury but helped the Saints keep a clean sheet to leapfrog the Reds and win their group.
The draw for the second round takes place on Thursday (10:30 GMT).
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Sunderland's development squad qualified for the second round of the Checkatrade Trophy after beating Notts County 2-1 thanks to a late comeback.