The Baggies host Ole Gunnar Solskjaer's side on Saturday with only three points separating them from their 19th-placed opponents.
In one of the tightest relegation battles in recent years, there are only 12 points between Stoke City in 10th and the drop zone.
Pepe Mel's side have just eight games remaining to retain their Premier League status, but midfielder Mulumbu insists West Brom are solely focused on the visit of Cardiff.
"The only thing that will do is the victory - it is do or die," he told the Daily Mirror.
"We're not looking too far into the future. For us there is only game - Cardiff is a final.
"We are aiming to be defensively strong. It has been a long time now since West Brom kept a clean sheet.
"If we don't concede I think we will win the game."
Mulumbu acknowledged the significance of the game and, with an average attendance of around 25,000 at The Hawthorns this season, he expects Cardiff to receive a hostile welcome.
"I hope our fans can make The Hawthorns a scary place for Cardiff to play on Saturday," he added.
"We know we are at home - and the opponent feels that. We need to show Cardiff this is going to be a long afternoon and we're there to win.
"We want to do everything to stay in the Premier League and that's for the fans because they don't deserve to go into the Championship.
"This is one of the most important games for West Brom because this can make life really difficult for Cardiff and boost us."
After Baggies boss Mel revealed Victor Anichebe will face a late fitness test, Mulumbu admitted the striker could play a crucial role in Saturday's clash.
"Anichebe is a different type of player and we are trying to get him back for the game," he said.
"If he is not fit enough to start at least he will be on the bench to come on. He is an important player for us."