The only goal of the game came from Granit Xhaka and it was enough for the win over PSV.
The result leaves Mikel Arteta's side with a five point lead at the top of the group.
The rearranged game that was originally scheduled to be played on September 15 was postponed due to the death ofQueen Elizabeth II.
The performance of PSV's Argentine goalkeeper Walter Benitez made for a nervy evening as he made a number of saves.
Swiss international Xhaka drove a low effort into the bottom left corner to break the visitors' resistance.
If they get a point in the Netherlands next week, they will be confirmed as group winners.
The arrival of van Nistelrooy's side at the Emirates provided the toughest test of the season so far for the north London club.
Arteta will be happy that his side passed it with flying colors, but he will be disappointed that the score didn't reflect their dominance.
PSV didn't offer much going forward with a reported Manchester United target.
Instead of taking the game to their opponents, the visitors were penned back and spent a lot of time trying to stop the flow of attacks from the north London club.
Eddie Nketiah had six of the team's 25 attempts on goal, failing to hit the target once, and Xhaka had a chance to convert from an easier position in the first half, but he missed.
Jesus was also wasteful in front of the goal.
The Brazilian prodded a weak left foot effort into the arms of the former Nice goalkeeper after weaving past two defenders and saw the former Nice goalkeeper save another goalbound effort with his foot.
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