Ole Gunnar Solskjaer's side were awarded a penalty at the start of the second half, only for it to be overruled by VAR as Marcus Rashford was marginally offside before collecting a pass from Bruno Fernandes and being fouled by Kyle Walker inside the box.
United went close to scoring on another couple of occasions but were indebted to a David De Gea save in the first half, to thwart Riyad Mahrez, after he latched onto a clever ball by Kevin De Bruyne.
Bruno Fernandes fired a shot that was held by Ederson in the closing stages but there was to be no breakthrough in a tense affair.