A first-half goal by Chris Greenacre gave Tranmere all three points against Oldham who had two men sent off.
Greenacre headed into the top corner in the 25th minute after Kevin Ellison headed on Chris Shuker's cross.
Four minutes after the break, Greenacre spurned a chance from 10 yards before home keeper Gavin Ward turned aside an angled header from Maheta Malongo.
Chris Taylor saw red on 88 minutes for fouling Calvin Zola and Neil Eardley followed for kicking the ball at Zola.
Tranmere: Ward, Stockdale, McCready, Goodison, Cansdell-Sherriff, Shuker, Mullin, McLaren, Ellison (Tremarco 69), Taylor (Zola 84), Greenacre.
Subs Not Used: McAteer, Davies, Achterberg.
Goals: Greenacre 24.
Oldham: Pogliacomi, Eardley, Swailes, Haining, Edwards, Wood, McDonald, Rocastle (Taylor 72), Wellens, Liddell (Warne 72), Molango (Hall 80).
Subs Not Used: Howarth, Stam.
Booked: Taylor, Eardley.
Ref: R Olivier (W Midlands).