The Lions thought last weekend’s victory over Hartlepool would confirm their League One status but they were dealt a brutal blow when Prutton volleyed home after 70 minutes.
And United midfielder Andy Hughes added to the Lions misery eight minutes later to seal the deal as Millwall slumped to within four points of safety.
The Lions nearly took an early lead when Ahmet Brkovic curled a free-kick wide after Paul Huntington brought down Paul Robinson.
And 22-year-old Craig’s misery continued after the break when his poor clearance allowed Prutton to open the floodgates with a superb 25-yard volley.
And substitute Hughes lashed home Bradley Johnson’s cross as Leeds won their fourth game in five.