Only four days after taking over from Brian Talbot, Moore watched his team brush past Vale with a goal from Will Haining and two more from loan star Kenny Cooper.
Vale were a poor shadow of the side which beat leaders Luton last week, and Oldham could have doubled their tally with a dominant display.
Cooper hit a quick double early in the second half to show the quality which saw Manchester United bring him over to England from his native Untied States.
Oldham almost took an early lead when Neil Kilkenny forced visiting keeper Mark Goodlad to tip his 25-yard shot over the bar.
However they did score on 27 minutes when veteran midfielder David Eyres sent a free-kick in from the left and Haining jumped highest ten yards out to head inside Goodlad's right-hand post.
The only time Vale tested Oldham's keeper was two minutes before the break. Michael Cummins thought his shot from the edge of the box was heading in yet Leslie Pogliacomi sprawled to his right to make a fine save.
That was the catalyst for Oldham to push for a second and they scored it seven minutes after half time through 20-year-old Cooper. He chased a throughball from Kilkenny and fired low past Goodlad from a tricky angle ten yards out.
The same two players combined to put Oldham 3-0 up as Kilkenny's shot from distance was spilled by Goodlad, who saw his mistake punished when Cooper tapped in the loose ball.
Oldham almost added a fourth when striker Chris Killen slammed a shot against the crossbar and Kilkenny was denied by a fine Goodlad save in the last two minutes.
On a day to forget for the visitors, Ian Armstrong went off with an ankle injury - Vale had used all three substitutes and ended the game with ten men.