Top-scorer Craig Davies made the breakthrough for Oldham but Calum Willock soon levelled and Vale were unlucky not to clinch victory in the second half.
The visitors hit the woodwork on two occasions as manager Lee Sinnott watched another encouraging performance from his new team.
Sinnott was pleased with the outcome, saying: "We did not come for a point but I am quite happy to take one.
"Port Vale did not have the best of starts this season but I would not be here if circumstances were different and I am trying to build up some confidence among the players.
"It is not a sprint but we are getting there and the table still does not concern me, even though everyone is eager to get things right straightaway."
Port Vale had an early chance for Luke Rodgers and Willock was also given space close to Oldham's goal without managing to test keeper Mark Crossley.
But Oldham had a bright spell which saw Lee Hughes have his headed effort ruled out for offside before Davies fired over the bar.
The home side went in front midway through the first half when Chris Taylor delivered a pin-point ball from the left and Davies rose at the far post to head in from close range for his ninth goal of the season.
Hughes had an effort cleared by George Pilkington, but Vale were level on 32 minutes when Willock was left unmarked eight yards out and he turned smartly to crash his shot into the top corner.
Vale's best chances after the break both ended in despair as Willock's angled drive came back off the inside of the far post and, in the 89th minute, substitute David McGoldrick also hit the post.
Oldham had an opportunity themselves but Deane Smalley blazed off target after visiting keeper Joe Anyon thwarted Davies.