Hughes: On the scoresheet
The Lions thought last weekend's victory over Hartlepool would confirm their League One status but they were dealt a brutal blow when ex-Nottingham Forest man 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 flew out of the blocks and nearly took an early lead when Ahmet Brkovic curled a free-kick narrowly wide after ex-Newcastle defender 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.
Things went from bad to worse for Kenny Jackett's men when substitute Hughes lashed home Bradley Johnson's cross as Leeds won their fourth game in five.