The damage was done in the opening 45 minutes as the Glovers took a 3-0 lead.
Stephen Arthurworrey and Simon Gillett had put the visitors two goals ahead before Yeovil made it three just before the break.
Sam Hoskins grabbed the goal and deep into additional time in the second half, substitute Kieffer Moore scored the fourth as Latics dropped out of the play off positions.
With the rain lashing down over SportsDirect.com, the first half could not have gone much worse of the home side.
With Latics having early chances through Daniel Johnson and Jabo Ibehre, they fell behind just after 20 minutes as Yeovil Town took the lead.
Arthurworrey rose above everybody and initially headed against the post but the rebound fell perfectly for the defender and he prodded the Glovers ahead.
Latics had a good chance to find a leveller soon after the goal but Ibehre could not get to the ball quicker than Yeovil goalkeeper Jed Steer.
The home side would rue that missed chance as the Glovers took a two goal lead just before the half hour mark.
Genserix Kusunga was caught on the wrong side of the attacker and Gillett fired past loanee Paddy Kenny to extend Yeovil's lead.
Latics again went close with efforts before the break. Brian Wilson volleyed straight at Steer whilst Mike Jones' drive from 25 yards just went past the goalkeeper's post.
A nightmare first half for the home side was capped off five minutes before the break as Gary Johnson's Yeovil Town made it 3-0.
Hoskins dispossessed defender Kusunga and stroked the ball past the onrushing goalkeeper as Latics headed into the break with their spirits dampened.
Manager Lee Johnson made two changes at the break as Carl Winchester and Dominic Poleon were introduced in place of Kusunga and Timothee Dieng.
Latics started the half with a lot more urgency and saw a penalty shout in the first minute of the half turned down. As the ball was whipped into the box, the ball seemed to hit an outstretched arm but the referee was unmoved.
Minutes later, Joseph Mills was hacked to the floor just outside the penalty area and the referee awarded Seth Nana Twumasi a booking.
Latics were struggling to create clear cut opportunities but just after the hour mark, Yeovil almost rewarded the home side.
Defender Nathan Smith smashed the ball against Arthurworrey as he tried to clear the ball and goalkeeper Steer had to save on the line to deny an own goal.
The Glovers really should have put the game beyond doubt on 70 minutes as former Latics youngster Tom Eaves rounded Kenny but fired wide when presented with an open goal.
The forward, who was a second half substitute, was not having the best of afternoon's in front of goal as he ballooned a shot past the post when set through on goal with 15 minutes remaining.
Latics were struggling to get behind the well organised Yeovil defence but almost found a way back into the game on 80 minutes.
The ball was fed forward to Johnson and he opened up his body and shot from the edge of the area but it just whistled over the crossbar.
Brian Wilson went close for Latics before the end of the 90 minutes, narrowly shooting wide from the edge of the box.
As the game moved into additional time, the Glovers made it four as Moore smashed home from the edge of the box to compound Latics' misery.
The referee blew the final whistle as Latics dropped out of the play off positions.
Oldham Athletic: Kenny, J.Wilson, Elokobi, Kusunga (Winchester 46'), Mills, B.Wilson, Dieng (Poleon 46'), Jones, Johnson, Philliskirk, Ibehre.
Subs not used: Rachubka, Tidser, Dayton, Mellor, Morgan-Smith.
Yeovil Town: Steer, Smith, Edwards, Hayter (Eaves 68'), Foley, Hoskins (Leitch-Smith 72'), Twumasi, Clarke, Nugent, Gillett (Moore 80'), Arthurworrey
Subs not used: Moloney, Berrett, Krysiak, Smith
Goals: Oldham Athletic 0-4 Yeovil Town (Artherworrey 21', Gillett 28', Hoskins 40', Moore 90+1')
Attendance: 3,706 (111 visiting supporters)