The visitors were rewarded when they took the lead on 11 minutes, Jay Simpson flicked a pass from Jem Karacan into the corner of the net.
And it should have been 2-0 three minutes later when Millwall again opened up the home defence, but Simpson’s shot went straight into the arms of Arran Lee-Barrett.
Hartlepool had an Andy Monkhouse goal disallowed for offside on the half-hour as they tried to get back into the game.
But just before half-time David Martin hammered a shot against the crossbar to again nearly double the visitors lead.
There was more from the home team in the second-half, but Joel Porter headed over, Antony Sweeney’s weak shot was saved and Willie Boland’s 20-yard effort was wide.