Lee's Latics are now all but guaranteed survival in League One, but defeat was a major blow to Yeovil's automatic promotion hopes.
The Johnsons were only the second father and son duo in Football League history - and the first since the early 1970s - to come up against each other in management.
Oldham striker Matt Smith settled a closely-fought contest, heading home Lee Croft's corner in first-half injury time for his 10th goal of the season. Lee Johnson, the league's youngest manager at 31, said: "This is a fantastic result for us and we deserved it.
"Any team managed by my old man is going to give you a tough game and I hope Yeovil go up through the play-offs.
"We had a little cuddle at the end and I felt for him because he was upset with the result, but for us it's all about three big points.
"During the game I didn't think once about him being my dad, but we will probably spend some time together tomorrow (Wednesday) unless I decide to play in our reserve game.
"There was a big build-up beforehand and a lot of attention on the two of us, but really I was more focused on getting the lads ready.
"The players didn't half work hard and I knew we would score from a set-piece because we had a good 20 inches in hand on Yeovil if you add up all the players. We have a great chance of staying up now and one point will do it, but we won't be complacent."