Oldham's game plan was dented straight away when Mark Bonner was forced out of the match after a collision with Rob Scott left the midfielder clutching his arm.
A failure to close down Richie Wellens led to Chris Killen receiving the ball inside the area but his shot was deflected over the crossbar by the saving tackle of George Pilkington.
Luke Beckett's excellent record against Port Vale continued in the 15th minute when Marc Tierney's deflected pass found the striker 10 yards from goal, leaving him to finish low to Mark Goodlad's right.
Any chance of Vale scoring looked doubtful, as both Chris Birchall and Danny Sonner were limited to shooting no closer than 25 yards out.
A heavy challenge on Sonner on the edge of the box in the 40th minute ricocheted into the path of Billy Paynter but he failed to capitalise on his side's best chance of the half, shooting weakly wide.
The Valiants finally threatened the away goal after the break when Michael Cummins' cross from the right was met by the head of Sonner, but Chris Day was on hand to push the ball around his left post.
Port Vale ended their goal drought after 71 minutes when Sam Collins' low drive from just inside the area found the boot of Cornes, who lifted it into the roof of the net from close range.
However, their joy was short lived when a half-cleared Andy Liddell corner fell to Killen and the striker buried the ball into Goodlad's bottom right corner to restore the lead.
Vale's dogged determination paid off in injury-time when loanee Cornes arrived at the back post to meet George Abbey's cross and power a header past Day.