Ten-man Newry held an Institute side which must now plan ahead for a Carling Premiership promotion/relegation play-off with Donegal Celtic.
Paddy McLaughlin fired in a 25th minute opener before City's Cullen Feeney was red-carded on 41 minutes after a last-man foul on David McClements.
Andy Graham levelled seconds after the interval when his hopeful shot slipped through the hands of Alan Ryan.
DC are sure of second place in the Championship after winning on Saturday.
The west Belfast side still have a chance of winning the title, depending on how Loughgall fare in their final three games.
If Donegal Celtic clinch top spot they will be automatically promoted to the Carling Premiership with Institute relegated.
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