West Brom failed to put Millwall to the sword after hitting the bar twice in a 0-0 draw but the hosts were also indebted to goalkeeper Alex Palmer for his first-half penalty save.
Palmer denied Millwall forward Zian Flemming from the spot in the 27th minute, before Alex Mowatt and Brandon Thomas-Asante hit the woodwork after the break.
The result means West Brom have gone four games without a win, although they have drawn their last three.
Millwall kept a second successive clean sheet after beating Rotherham 3-0 in midweek.
On a day when The Hawthorns rose to salute late West Brom midfielder Ian Hamilton, who died recently at the age of 55, both sides failed to spark in a forgettable first half featuring too many mistakes and too few chances.
West Brom head coach Carlos Corberan made five changes from Wednesday’s 2-2 draw at Watford, but those recalled barely suggested they were able to improve things.
After the break West Brom stepped up a gear and had several chances to take the advantage only to be denied by some vigilant Millwall defending.
Millwall almost took a second-minute lead in bizarre circumstances.
Palmer was forced to tip the ball over after his clearance from a back pass hit striker Duncan Watmore and sailed dangerously close to goal.
Grady Diangana – looking to make a positive impression on his first start of the season – had the home side’s first chance with a low drive that was deflected wide.
The first half burst into life when Millwall were awarded a penalty.
Ryan Longman’s corner was handled by Kyle Bartley, who had twice been off for treatment for a facial injury following an aerial clash.
But Palmer got a good hand to Flemming’s spot-kick diving low to his right.
From the resulting corner swung in by Longman, Tom Bradshaw’s glancing header drifted wide of the far post.
West Brom hit the second half running and twice went close to the breakthrough in the 50th minute.
Thomas-Asante’s shot was saved by goalkeeper Bartosz Bialkowski and Matt Phillips’ follow-up was blocked by Longman after Diangana crossed.
Erik Pieters kept up the hosts’ momentum with a low drive from 25 yards that Bialkowski fumbled, Thomas-Asante unable to find a team-mate from the loose ball.
West Brom continued to look the more likely scorers – especially in the 63rd minute when Mowatt’s curling free-kick rattled the underside of the crossbar.
In the scramble that ensued, Semi Ajayi glanced just wide.
Albion hit the woodwork for the second time in the 73rd minute.
This time Thomas-Asante’s header was deflected onto the bar after Conor Townsend crossed, Phillips nodded back into the danger area and two Millwall defenders got in the way.
Right at the death, Thomas-Asante failed to get a proper connection with a close-range header from Mowatt’s deep cross.
