The visitors were reduced to 10 men after half-an-hour when Semi Ajayi was given his marching orders for a deliberate handball, but the Clarets were unable to make their numerical advantage count.
Instead, it was the Baggies who almost wrapped up maximum points as Sam Allardyce's men went for broke after the break.
Ainsley Maitland-Niles fired over the bar when cutting on to his right foot, Mbaye Diagne hit the bar and Matheus Pereira saw his effort cleared off the line by James Tarkowski.
Here are the RATINGS.
Ainsley Maitland-Niles fired over the bar when cutting on to his right foot, Mbaye Diagne hit the bar and Matheus Pereira saw his effort cleared off the line by James Tarkowski.