The Clarets' winning streak ground to a disappointing halt as Millwall impressively ended their Turf Moor torment to deliver a set-back to Burnley's play-off hopes.
The Lions hadn't won at Burnley in seven attempts in a run stretching back to 1997.
And despite beating Championship leaders QPR in mid-week, a record on no away wins since November didn't bode well for Kenny Jackett's men.
But with Burnley failing to find the form that had brought them five wins in their last six games, three second-half goals left the Clarets licking their Lions-inflicted wounds.
Millwall captain Paul Robinson led by example as he twice headed home following corners and Andros Townsend rubbed it in three minutes from the end as the gap between Burnley and the play-off places again extended to four points.
Results elsewhere slightly softened the blow for the Clarets as QPR were the only side above them in the table to win.
Rare sight of goal
But having missed such a golden opportunity to close on the top six, the Clarets must bounce back from only a second Championship defeat under Eddie Howe when they face struggling Coventry City at Turf Moor next Tuesday night.
After winning their last three games Burnley were not surprisingly unchanged and having scored on his debut with the Clarets' mid-week winner at Hull, Delfouneso almost made an instant impression at Turf Moor with a header that hit the woodwork after just 13 minutes.
Anticipating Jay Rodriguez's knock-down from a Tyrone Mears' free-kick, Delfouneso steered a header just too high from a rare early sight of goal.
Taking their time to find anything like top gear it wasn't until mid-way through the first half that Burnley built up any sustained pressure.
Tough home debut
But then in a frenetic six-minute spell they created a flurry of chances to take the lead.
The first came Rodriguez's way after Jack Cork and Ross Wallace had opened up the Lions' defence for Wallace to feed Rodriguez for a shot which had goal written all over it until the ball nicked off a defender and flew just past the post.
Down but not out
Dean Marney then fired over after Burnley had passed their way through the Millwall midfield before Delfouneso's next major contribution saw him ferry the ball to Mears to burst into the box and curl an effort just over the bar.
Marney then just failed to get enough on an attempted header from a Chris Eagles' cross as the Clarets threatened to take control.
But having come through that spell unscathed Millwall had their best moments of the half and after a half-chance for top scorer Steve Morison was grabbed by the back-pedalling Lee Grant, midfielder James Henry weaved his way into the penalty area to curl a left footed shot just wide eight minutes before the break.
If that was a reminder for the Clarets that they needed to raise their game it appeared to have the desired effect at the start of the second half as they started with a much better tempo.
Wallace and Marney both let fly with efforts from just outside the penalty area as Millwall were pushed onto the back foot.
But again just as it seemed that the breakthrough might be on the way the Lions roared up the other end and snatched an unlikely 1-0 lead as captain Paul Robinson stooped to head in a corner at the back post.
Drawing a blank
Things might have got worse had Morison picked out Kevin Lisbie after breaking clear and Howe waited only until the hour mark to send on Chris Iwelumo to offer a different angle of attack as the Clarets struggled to find a way back into the game.
Wade Elliott then came on for Delfouneso but Millwall looked the more likely to get the next goal and so it proved with 20 minutes to go as the visitors doubled their lead.
The Clarets had looked vulnerable from set-pieces and having survived when Lisbie's shot was deflected wide following a free-kick they conceded from the corner that followed.
Not Burnley's day
This time it was played short but again Robinson found the space to head downwards and into the back of the net to signal the Clarets' fourth home defeat of the season.
Marney shot over when a goal might have given Burnley the impetus to mount a late fightback but a disappointing afternoon was compounded three minutes from time when Townsend broke clear to rifle home Millwall's third.
Burnley: Grant, Mears, Fox, Carlisle, Duff, Marney (Alexander 90), Cork, Eagles (Iwelumo 60), Delfouneso (Elliott 68), Rodriguez, Wallace. Subs: Edgar, Bartley, Bikey, Jensen.
Millwall: Forde, Dunne, Craig, Robinson, Ward, Mkandawire, Trotter, Henry (Eastmond 90), Morison, Lisbie (Rowlands 79), Townsend (Barron 88). Subs: Hackett, Barron, McQouid, Marquis, Mildenhall.
Referee: Eddie Ilderton.