Charlton started positively and saw an early corner headed away at the near post.
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With 10 minutes played Oxford had their first sustained attack of the match, but they failed to make the most of a succession of corners.
Simon Church then pushed on and tried his luck with a left-footed shot that flashed wide.
However, with the match heading for 0-0 at the break, Charlton struck twice. Church found Yann Kermorgant who buried his shot from 20 yards, before Green found the top corner from close range for a second in the space of three minutes.
The home side made a good start to the second half, although they were unable to trouble Ben Alnwick. That cost them with an hour played as Kermorgant curled his second of the night into the top corner.
Green almost added a fourth, but his powerful effort was just wide of the post.