Albion battled past storm Ciara and a physical Milwall side to extend their lead at the top of the Championship.
In awful conditions at The Den, it was Albion who blew away their opponents with a stylish away day performance.
Filip Krovinovic scored his second of the season in the first half before Dara O'Shea headed in his first goal for the Baggies late on to seal the three points.
Baggies boss Slaven Bilic praised the character of his players after they easily navigated what looked like being a potential banana skin.
"The performance is what pleases me the most, it is why I'm emotional now," said Bilic.
"I said to the guys, it has to be like this, this is the minimum standard now we have to do in a physical way. This makes you happy and confident.
"To come here and not just match them, but better them in a physicality against a team who are best in the league for that, that means something.
"If it's like that you have more chance to get a result. I'm extremely pleased with everybody, every single part of the squad. We were good."