Mason Bennett grabbed the first goal of the game as he prodded into the net following a free-kick.
Benik Afobe then added a second shortly after, twisting past the defence and finding the bottom corner.
Story of the match
He replaced George Evans in the Millwall eleven as they looked to grab their first win of 2022.
The Baggies started the brighter of the two teams as they flooded their attacking third with numbers.
They aimed to get the ball out wide quickly to produce crosses into the box to find their new signing, Carroll.
Albion continued to press on in search of an opening, this time it was Caroll who the ball fell to following a headed clearance.
Mowatt once again caused havoc from a set-piece, as he took a quick throw after spotting the run of Furlong, who flashed a ball across the face of goal, only just evading the onrushing attackers.
The game became more scrappy as the first half drew to a close, as McNamara crossed a looping cross towards the back post, only for Scott Malone to balloon his shot over the bar as he rushed in.
McNamara again was central to the Lions’ attacking play, this time he was played through by Burke, the right-back placed a pass across the area that only just evaded Afobe.
The home side came out the stronger side as Afobe skied a close-range shot following a knockdown from Burke.
The on-loan blades man found himself in on goal following a scramble in the Albion box, goalkeeper David Button then produced a superb save to deny him.
It was Burke again who had a fantastic chance to take the lead, Jake Cooper's cross-field pass sought him out, but the forward's touch was too heavy to get around Button.
Irish forward Robinson almost made an instant impact, his low shot almost caught Bialkowski out at his near post, as he tipped onto the woodwork.
As the hosts continued their dominance, Bennett managed to touch down Sean Hutchinson's flick-on.
A goal meant the Lions' tails were up, Afobe's pressure meant he found himself one-on-one with Clarke on the edge of the area.
He twisted the defender inside and out, producing a cool finish past Button to double their advantage.
Albion had an opportunity to eat into their tally, as Diangana crossed towards the back post, only for Carroll's launched header to bear straight at the 'keeper.
The Baggies fans showed their frustrations towards the end of the game by halting play twice, throwing both a flare and a torn out stadium seat onto the field of play.