The 31-year-old, the son of Yeovil boss Gary Johnson, is the youngest manager in the Football League following his appointment on Monday.
And he saw his new side go in front at Boundary Park after 17 minutes on Tuesday night through Robbie Simpson's header, with Jean Yves Mvoto nodding home a second shortly before the half hour.
Jose Baxter finished the visitors off in the 69th minute.
The win took Oldham a point above the drop zone.
Gary Johnson could not match his son's success, though, as his Yeovil side slipped to a 2-0 defeat at home to fellow promotion hopefuls Swindon.
Adam Rooney's 77th-minute penalty opened the scoring and James Collins made it two deep into stoppage time at Huish Park as the Robins moved to within a point of the top two, three ahead of their opponents.
Bury moved off the foot of the table, and sent Portsmouth bottom, as two late goals earned them a 2-0 win at home to Stevenage.
Steven Schumacher missed a 20th-minute penalty and it looked like that might be costly until Craig Jones broke the deadlock in the 82nd minute at Gigg Lane and Jonson Clarke-Harris made the points safe in the last minute.
Finally, Mathias Pogba scored twice as Crewe came from behind to beat MK Dons 2-1 at Gresty Road.
Patrick Bamford headed the Dons into a 31st-minute lead, but Pogba levelled nine minutes later and got the winner six minutes from time.
The Dons finished the match with 10 men thanks to Antony Kay's 86th-minute sending-off.
