Ba broke the deadlock in the 33rd minute when Mike Williamson headed Danny Simpson's free-kick across the face of goal to leave Ba with the simplest of chances.
Magpies boss Alan Pardew made a series of changes at half-time and Monaco almost equalised shortly after the restart when Valere Germain headed against the post.
Ba almost extended Newcastle's lead in the 71st minute when he headed just wide from a Ryan Taylor corner.
And substitute Gabriel Obertan came close in the dying seconds when he burst clear but fired straight at Monaco keeper Daniel Subasic.
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