McLean's effort spared the blushes of strike partner Craig Mackail-Smith who had steered a great headed chance tamely wide only moments earlier. And it provided a welcome source of cheer on a night in which Darren Ferguson's side suffered a double injury blow.
Their woe began after only nine minutes when influential central defender Gaby Zakuani sustained a suspected neck injury after falling awkwardly following an aerial challenge. The Democratic Republic of Congo international required eight minutes of treatment before being stretchered off and taken to hospital for an x-ray.
The home side were restricted to long-range efforts during the opening period with Paul Coutts and Charlie Lee both testing Williams from distance. But Ferguson's men suffered a further blow just before the break when recent recruit Lee Frecklington hobbled off with a hamstring problem.
And the promotion-chasers also received a lucky escape in the fourth minute of first-half stoppage time when keeper Joe Lewis denied Danny Graham at point-blank range following a free-kick delivery from the dangerous Lewis Neal. Graham again went close soon after the restart when flashing an angled half-volley across the face of the target, but Posh gained the upper-hand and hit the front courtesy of McLean.
Whelpdale forced a fine save from Williams with a late 20-yard blockbuster before Mackail-Smith stung the visiting keeper's palms in the dying moments. But one goal proved to be enough for Posh to remain in the thick of the promotion race.