The Baggies created some glorious goalscoring opportunities and really should have won the game – with Mbaye Diagne and Matheus Pereira, in particular, guilty of missing some huge chances.
Here we rate the Baggies players following their trip to Turf Moor.
With Burnley having just one effort on target, Johnstone didn't have an awful lot to do here. When he was involved, though, he looked steady and assured. 6
Part of a back-four that secured a confidence-boosting clean sheet, Furlong largely defended well at right-back. He also went close with a curler from the edge of the box. 7
Ajayi started well but then got his marching orders for handball as he tried to atone for Conor Gallagher's loose pass. It was unfortunate, but by the letter of the law he had to go. Thankfully, he will only miss one game. 5
Jay Rodriguez and Matej Vydra got very little service from their Burnley team mates. But when they did, Bartley coped with their threat well. 7
Another well-rounded display from the full-back who has come on leaps and bounds defensively. Not able to get forward as much as he would have liked with the team having 10 men. 7
Once again the Turkish international screened Albion's defence expertly. Yokuslu's brilliance was epitomised when he won three crunching sliding tackles in the space of just a few seconds. What a signing. 8
The Chelsea loanee played well in a tenacious display that saw him refuse to give Burnley any time to breathe. He has to be marked down, though, for that poor pass to Ajayi. 6
At the heart of everything his team did well, Maitland-Niles was the driving force as Albion pushed and pushed for a winner. He broke lines, created chances and also went close himself in an influential, man of the match display. 8
Got a chance to start with Robert Snodgrass injured. But Phillips didn't offer a great deal before being substituted for Dara O'Shea following Ajay's red card. 5
How did he not score? Diagne did brilliantly to go past James Tarkowski and get himself in a shooting position just six-yards out. Somehow, though, he fired over despite the goal being at his mercy. He needs to improve his conversation rate, but there is no doubt Diagne is a very dangerous player who has improved Albion significantly. 6
How did he not score... twice? Pereira looked destined to simply tap in a Diagne cross but fluffed his lines. He also saw a shot from four yards cleared off the line by Tarkowksi. Very dangerous but lacking a cutting edge. 6
Dara O'Shea (for Phillips, 30)
Thrown on after half-an-hour, O'Shea defended superbly following his introduction. The 21-year-old read the game well and as was also a commanding presence in the air. 7
Subs not used: Button, Peltier, Livermore, Sawyers, Robinson, Grant, Diangana, Robson-Kanu.