Hartlepool failed to cash in after being handed a chance to take an early lead when Millwall defender Tony Craig handled Joel Porter's flick to give away a penalty.
But goalkeeper David Forde dived to his right to beat out Porter's spot-kick as Millwall breathed a sigh of relief.
The home team came back and two goals in two minutes, both from Antony Sweeney, put them in control.
Sweeney struck first on 23 minutes with a stunning 25-yard volley as a Millwall clearance landed at his feet, then he finished neatly after racing out of his own half with Porter, who supplied the telling pass.
Millwall gave themselves a lifeline on 62 minutes when Harris curled a 20-yard free-kick round the wall into the top corner of the net. Harris struck again on 67 minutes when he cut inside from the left and finished from a tight angle, and he chalked up his hat trick on 72 minutes when he smashed the ball in after a mistake by Sam Collins.