The Johnsons were only the second father and son duo in Football League history - and the first for over 40 years - to face each other as rival bosses.
And it was 31-year-old Lee who won the family battle, giving Oldham's survival hopes a massive boost and denting Yeovil's bid for automatic promotion.
Yeovil, already guaranteed a play-off spot, went close early on through Angelo Balanta.
But they soon came under pressure as Oldham's Matt Smith had a header cleared off the line by Richard Hinds before sending another effort over.
Visiting keeper Marek Stech made a fine save from David Mellor's free-kick, but Oldham led on the stroke of half-time when Smith met Lee Croft's corner with a stooping six-yard header.
Yeovil created little despite their second-half possession, substitute Vitalijs Maksimenko wasting their best chance in the 86th minute.