Both sides were happy to enjoy spells of possession during the opening stages without creating many chances.
The winger eventually broke the deadlock with 26 minutes on the clock when he beat goalkeeper Steve Harper with a calm finish following a ball over the top.
Despite looking toothless in front of goal, Newcastle grabbed an equaliser with the last kick of the half thanks to Taylor's set piece.
The visitors dominated for much of the second half and had a good opportunity to take the lead when Papiss Cisse's effort was saved by a recovering Itandje after the goalkeeper had fumbled Gabriel Obertan's cross.
The shotstopper was called into action again with 15 minutes to play as Romain Amalfitano was smothered following a quick counter attack.
There was a late chance for Atromitos in the form of Kostas Giannoulis's volley, but the defender could only hit it wide.
The second leg at the Sports Direct Arena takes place next Thursday.