Cheltenham started very brightly against Iain Dowie’s away-day specialists and Mark Yates found the net after just two minutes with his seventh goal of the campaign.
Jamie Victory’s long throw was flicked on by Alsop and Yates connected well with his left foot to give Bobby Gould’s men a dream start.
Oldham then began to show why they are contenders for automatic promotion to Division One, turning on the style and posing a constant threat to Shane Higgs’ goal.
Higgs acquitted himself well but he could do nothing to stop David Eyres’ powerful header from a Josh Low corner on 31 minutes.
The frenetic action continued with both sides pushing for a second goal. Higgs denied Clyde Wijnhard and Wayne Andrews as the Latics finished the half on top.
The second half saw Jamie Victory moving inside to partner Mike Duff in the heart of the Robins defence, with David Bird moving to left-back and Steve Jones switching to right-back.
Oldham ’keeper David Miskelly blocked an Alsop effort and John Brough was unlucky to see his long range lob drift wide of an unguarded net.
Antony Griffin joined the action, filling in at sweeper as Steve Jones made way. Grant McCann fired a series of dangerous free-kicks into the Oldham penalty area, but the Latics’ defence held firm.
Oldham then had a great chance to claim all three points as they caught Cheltenham on the break. Higgs narrowed the angle well and blocked a Wijnhard shot with his feet. The ball fell kindly for the former Ajax front man to have another bite of the cherry, but Jamie Victory made a fine block on the line to keep the scores even.
Substitute Marvin Brown soon made an impact, firing in a wonderful long-range shot that brought out the best in Miskelly, who acrobatically tipped the effort over the bar.
The final whistle blew to confirm a precious point for Cheltenham and with it, the home side’s third consecutive draw.