Aleksandar Mitrovic was dismissed in the 16th minute for a studs-up challenge on Francis Coquelin.
Coloccini inadvertently put the ball in his own goal in the 52nd after clipping Alex Oxlade-Chamberlain's shot.
Newcastle remains without a league win after four games under new manager Steve McClaren, with the only success coming in the League Cup.
Arsenal has seven points from four games.
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