Peter Hartley, Adam Boyd and Armann Bjornsson were on target as Pools opened up their unassailable lead within 29 minutes.
Hartlepool took the lead with 13 minutes gone when a Sam Collins cross was headed out to the lurking Hartley who fired a right-foot shot into the net from 25 yards.
The second goal arrived on 22 minutes, Boyd making the most of space between goalkeeper and defence to nip around David Forde and roll into the net from an angle score.
Giant striker Bjornsson then completed the rout, deftly heading home at the far post from a McSweeney cross.
Millwall, with three up front in the second half, went closest when Lewis Grabban twice had shots blocked by Flinders from six yards.