Millwall slipped to their first defeat of 2013 as goals from Sam Vokes (19mins) and Danny Ings (57mins) secured victory for Burnley at The Den.
It proved to be a bad day at the office for a Lions side that struggled to get going in the freezing conditions.
Burnley were excellent value for the win and ensured that manager Sean Dyche's incredible record against his former club now stands at 11 wins and one draw since leaving The Den in 2002.
"The result didn't please me, I don't think we did enough to get anything out of the game. Burnley showed more hunger and desire for the game today than we did and that's disappointing.
I thought we started the game poorly and they got behind in wide areas too easily. The first goal was a prime example of their player getting past Henry and Smith to deliver for Vokes to score. We didn't defend well, defend for our life which we can do when we play well."
On a forgettable afternoon for Millwall, the home side looked sluggish and in the opening half an hour could have been further behind than just the one goal scored by Vokes.
Lions keeper David Forde was so nearly made to pay on 16 minutes when he dithered on the ball, lost possession to Vokes, whose cross was met by Ross Wallace, but his tame shot was gathered by the stopper.
And just two minutes later Millwall were behind as Junior Stanislas pounced on a poor second touch from James Henry.
Stanislas weaved his way through the home rearguard and his cross was turned in by Vokes, with the ball going through Forde’s legs.
Millwall tried to build up a head of steam as the half progressed, but rarely threatened Lee Grant in the Burnley goal, whose only save in the opening 45 minutes came to deny Liam Trotter's first-time hooked shot from a Martyn Woolford delivery.
New signing Nathan Tyson replaced fellow home debutant Woolford after the break and Millwall could have levelled on 50 minutes when Henry’s mazy run and cross was fired well over from close range by Andy Keogh.
An inviting Henry delivery was inches away from Dany N’Guessan and Tyson as The Lions carved out another half-chance, but they were stung when Ings stole in ahead of Mark Beevers and Adam Smith to head Kieran Trippier's cross past Forde for number two.
Millwall had Forde to thank for preventing a third goal when he made a smart stop from sub Keith Treacey 20 minutes from time.
Jackett's men went close to grabbing a lifeline with 10 minutes remaining but Trotter's goal-bound shot was blocked by Trippier on the line to block his piledriver and with that went any real chance of The Lions clawing their way back.
Forde, A.Smith, J.Smith, Abdou, Shittu, Beevers, Woolford (Tyson, 46mins), Trotter, Keogh, N'Guessan (Marquis, 66mins), Henry. Subs not used: M.Taylor, Dunne, Osborne, Racon, Wright.
Grant, Trippier, Shackell, Lafferty, Ings (Paterson, 90+3mins), McCann, Wallace, Stanislas (Treacey, 70mins), Vokes, Edgar, Marney. Subs not used: Jensen, O'Neill, Bartley, Stock, Anderson.
Vokes (76mins), Ings (79mins)
Vokes (19mins), Ings (57mins)
Att: 9,384 (away 579)