Three players were dismissed as City edged out the Bannsiders in the Carling Premiership game on Tuesday night.
A Davy Munster own goal put the visitors ahead before Andy Graham netted on his first start for Newry.
Bannsiders striker Rory Patterson was sent off on 63 minutes and he was followed by Newry's Stephen Ferguson and Coleraine's Gareth Tommons.
Matthew Hazley, also making his first Newry start, fired home the winner from 15 yards after 75 minutes.
The opener came on 10 minutes when Andy Coleman saved a Tommons shot with his legs, only for the ball to hit off Munster and find the net.
Graham equalised after 26 minutes with a diving header from Chris Morgan's cross.
Patterson was dismissed for dissent with Ferguson also getting a straight red card four minutes later for a bad challenge on Michael Hegarty.
Tommons was sent-off after two yellow cards to make it three sent off in eight minutes.
Hazley won it with 15 minutes left to give Newry their fourth win of the league campaign.
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