Posh's victory owed a lot to good fortune after they had taken the lead in the 36th minute when a Yeovil clearance had struck Craig Mackail-Smith in the face and rebounded out.
Mclean latched on to the loose ball and his drive flew past Yeovil goalkeeper Josh Wagenaar and into the bottom-left corner of the net.
Yeovil were generally on the back foot with McLean always dangerous but had their chances - the best of which came in the 14th minute.
Danny Schofield brought a great save from Posh goalkeeper Joe Lewis when he met a cross from Paul Warne.
Yeovil stepped up the pressure in the search for an equaliser and almost got it in the 77th minute when Terry Skiverton joined in an attack and had a close-range effort cleared off the line by Craig Morgan.