Johnson - at 31, the youngest manager in the Football League - celebrated his first game in charge by watching the Latics cruise to victory at Boundary Park and climb out of the relegation zone.
Both sides side could have grabbed an early lead on Tuesday night as Steve Howard and Peter Hartley went close for Pools, while Oldham's Jose Baxter was twice denied by saves from Scott Flinders.
But it was Baxter who set up Oldham's opener after 17 minutes when his pinpoint left-wing cross was headed in from six yards by Robbie Simpson.
Oldham doubled their lead in the 27th minute, another fine Baxter cross being powered in from 10 yards by the head of Jean Yves Mvoto.
It was 3-0 after 70 minutes as Lee Croft teed up Baxter for an emphatic 18-yard drive past the helpless Flinders.
The result ended Oldham's three-match losing run, but Hartlepool are without a win or a goal in five matches.