Daniels, on loan from Spurs, grabbed his second league goal of the season and sunk battling Oldham, who had plenty of possession but no cutting edge.
It was the visitors who created the first real chance when Gary McDonald ghosted in at the near post but shot wide.
Orient responded and took the lead with their first real opportunity.
Daniels started the move and continued his run forward as Jason Demetriou knocked the ball into the path of striker Jabo Ibehre who headed it down for Daniels to rifle home from the edge of the area.
The super strike inspired the home side and Ibehre wriggled past Stefan Stam before firing over.
Then Orient top-scorer Adam Boyd sent a tame header wide of the target following a good cross from skipper Stephen Purches.
Oldham looked dangerous on the break and Andy Liddell shot wide but, with the home side on top, Demetriou should have stretched Orient's lead but was denied by a desperate tackle from Neal Trotman.
After the break Oldham dominated for long spells as Orient sat nervously on their lead.
But for all their possession, the visitors were unable to create too many clear-cut chances and it was Orient who almost grabbed a second when defender Alton Thelwell's effort was cleared off the line by McDonald.
As Oldham grew in stature, Deane Smalley headed over and the home side had to rely on breakaways.
From one such raid Boyd shot over, but it was Oldham who continued to press and in the closing stages Craig Davies shot over and then the hugely impressive Chris Taylor sent an effort skimming past the post.
But the nearest the visitors came to rescuing a point was in the 89th minute when Ryan Bertrand saw his effort cleared off the line by Demetriou.