Spackman made five changes to the side that lost against Brighton on Saturday, and handed debuts to Ali Fuseini and Chris Zebroski.
But the new-look side struggled to gel and fell behind to Clint Easton's stunning 14th minute strike.
Matt Jarvis' corner was only half cleared to Easton 30 yards out and the full-back unleashed an unstoppable drive past Chris Day.
Millwall had an immediate chance to level when Zak Whitbread rose to meet Alan Dunne's corner but his header flashed wide of the post.
The Lions appeared content to fire aimless balls to their front two but on 25 minutes Zoumana Bakayogo forced a decent save out of Scott Flinders after linking well with former Gills striker Darren Byfield.
Easton continued to pose a threat on the left and on the stroke of half-time found Guylain Ndumbu-Nsungu six yards out but the striker could not force the ball home.
Chances were at a premium throughout the game but the home side doubled their lead in the 64th minute.
Jarvis played a neat one-two with Mark Bentley before planting his shot past Day into the far corner.
The Gills missed a great chance to put the game beyond doubt when Jarvis found Michael Flynn in space on the edge of the box but the skipper blazed his shot high over the bar.
With time running out Spackman was forced to turn to his substitutes and threw on Marvin Williams and Poul Hubertz in an effort to salvage something out the game.
The move paid dividends when, in the 88th minute, Williams beat his marker and found Hubertz with a perfect cross for the Pole to head home.
Gillingham had to endure a nervous final few minutes as Millwall threw men forward.
Deep into injury-time Gills keeper Flinders threw the ball into touch for Byfield to receive treatment and when Paul Robinson refused to return it there were scenes of mayhem which continued long after the final whistle.