Liverpool substitute Alberto Moreno eyed up West Brom's unguarded goal but, like all other attempts during the second half, his shot was off target.
It was Liverpool's first win in eight attempts away at a Pulis side in the Premier League following Firmino's first half victor.
Lucas was central to an organised and balanced performance that saw Liverpool out-manoeuvre a well-drilled West Brom side and subsequently earn three valuable points away from home.
"And then we want to move onto 69. I am really happy about the performance".
The Brazilian attacker put in a strong showing, setting the tone with and without the ball for Liverpool, and nearly everything good on display for the Reds on Sunday afternoon involved Firmino, who has stepped up his game in the absence of Sadio Mané, Adam Lallana, and Jordan Henderson.
He was also unhappy with the response to that goal for the first 20 minutes of the second half but highlighted Albion's eighth-place position in the table and Liverpool's financial superiority.
So when the Brazilian headed past Ben Foster in first-half added time you knew what was coming.
Liverpool manager Jurgen Klopp: "It's one of the most hard places to go because you can't feel comfortable in one moment of the game".
"Somebody asked me which result would have kept me a little bit calmer in the last few minutes and I said only 4-0 after 86 minutes!"
"I can understand why".
Goalkeeper Ben Foster pushed forward in the final few minutes and that decision was almost punished but substitute Alberto Moreno missed an open net in the dying seconds.
BBC reports that despite that miss, Jurgen Klopp's side secured a fifth win in seven games, sending West Brom to a third straight defeat.
The Brazilian worldwide bagged his 11th Premier League goal of the season to emerge as the star performer for the visitors, while Simon Mignolet deserves credit for his second-half save in particular to deny Matt Phillips to preserve Liverpool's lead as he put in a great performance too.
"The goal really knocked us. I would have been happy for him, actually, if he'd scored this goal, but there was excitement until the end - which is pretty much always the way it is when we are involved".
"We came up against a (strong) side today, have a look at the resources they've got and we gave them a game".