Full-time from Glanford Park
Madden, making his 300th career appearance, got the ball rolling against the run of play on 36 minutes and added his second on 68 minutes, with Adelakun's 45th-minute effort squeezed between.
Scunthorpe made four changes to the team beaten at Rochdale the previous weekend, whilst Lions boss Harris handed centre half Shaun Hutchinson his full League debut, and also welcomed striker Steve Morison back to the bench after a spell sidelined with a knee injury.
Graham Alexander's side had dropped just four points on their home turf this season from 30 games and The Lions were under no illusion as to just how tough this match was going to be.
Right from the kick-off Scunny were on the attack and had a penalty appeal turned down with 11 seconds on the clock when Tom Hopper went to ground in the danger zone but referee Roger East waved play on.
Play swung up the other end and Iron's Paddy Madden was booked after two minutes for dissent after The Lions were awarded a free-kick 20 yards out following a handball, Joe Martin curled his resulting effort high and wide of the target.
It was certainly a lively opening and visiting keeper Jordan Archer had to be alert, firstly to deal with an awkward low cross slung across goal by 16 and then to gather a first-time shot from Madden that whilst on target, lacked power.
The best chance of the opening quarter of an hour came from midfielder Shaun Williams, letting fly with a dipping 25-yarder that Daniels in the home goal did well to tip over for a corner. Hutchinson powered a header narrowly off target after a short corner routine involving Shane Ferguson and Williams set up the defender at the back post.
Some determined play by O'Brien and Onyedinma saw the latter mange to toe poke the ball through to Gregory, but the frontman's crisp angled strike was clawed away by the keeper at full stretch.
However Iron took the lead just three minjutes later. Left-back Martin was booked for a challenge on Adelakun and from John Morris' deep free-kick, Madden's header looped over Archer and into the back of the net.
Millwall continued to press in search of an equaliser, but it was from another passage of play deep into the opposition's half that The Lions lost possession, lost their shape and were caught out on the counter with Adelakun lashing home at the second attempt after his initial effort had been blocked.
Facing a second-half mountain to climb, manager Harris introduced Morison and David Worrall for Onyedinma and Martin in a move that saw Ferguson drop to left-back, O'Brien slot in on the left of midfield and Morison partner Gregory up top.
The Lions enjoyed a decent spell of possession for a five-minute spell after the restart, but without really testing Daniels in the home goal as Iron defended resolutely.
Any hopes of producing a Bury-style fightback were quashed on 68 minutes with a goal gift-wrapped and served on a plate to Scunthorpe. Another quick counter attack looked to have been covered when keeper Archer came charging out of his goal and tried to place a header to a team-mate, but instead headed straight to Hopper who then unselfishly crossed for Madden to slot home the easiest of chances.
That third goal really knocked the stuffing out of a Millwall team who had regrettably been the architects of their own downfall.
Sub Calum Butcher and Gregory both had efforts blocked and an O'Brien shot on the turn from Ferguson's cross was blocked as The Lions came up against a rock solid rearguard that frustrated them until the very end.
Booking: Madden (2'), Wallace (47')
Scorers: Madden (36, 68'), Adelakun (45')
Bookings: Onyedinma (23'), Martin (36'), Hutchinson (61'). Thompson (75')
Att: 4,355 (away 365)
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