The teenager levelled after Reggie Welsh had opened the scoring for the Blues. A James Scanlon brace gave United a 3-1 lead before the break, with Obi-Martin completing his haul in the second-half.
United will now play the Gunners in the quarter-finals in March, with the 17-year-old almost certain to feature against his former club.
The sight of a former academy product scoring goals will be particularly painful for Arsenal, who have seen their own frontline decimated by injuries this season.