Plymouth remained on top of the second division despite dropping their first points for five matches.
Three players were sent off during an ill-tempered game in which both sides led: Oldham's John Sheridan and Plymouth's David Friio after clashing just before half-time, and Sheridan's team-mate Paul Murray, for two yellow cards, in the closing stages.
The nine Oldham players held out against Argyle's ten, though, to win a point that they probably merited after a dominant first-half performance.
The sendings-off spoiled a memorable day for Oldham centre-back David Beharall, who scored his first two goals for the club, either side of strikes from Plymouth's two local boys, Paul Wotton and Micky Evans.
Argyle went behind in a match for the first time since their defeat by Bristol City on September 30 after conceding a corner on their left flank. Sheridan curled it in, Ernie Cooksey flicked on, and Beharall bundled it past Jason Bent on the far post over the line.
The Pilgrims remained in arrears for just seven minutes, when the Latics conceded a free-kick on their right thanks to John Eyre's crude challenge on Peter Gilbert, and Wotton promptly curled the ball home from 40-plus yards.
With Sheridan and Friio dismissed, Argyle took the lead within six minutes of the second half starting. Wotton's short-corner was crossed to the far post by David Norris, nodded back in by Graham Coughlan, and headed home from close range by Evans.
Beharall's second was gifted to him by a mistake from young goalkeeper Luke McCormick, who fumbled a hopeful cross from Cooksey, leaving the former Newcastle man to thump home the loose ball.
Oldham were reduced to nine men in the 77th minute when Murray clattered into Peter Gilbert to earn his second yellow card.