It was another crucial moment in Liverpool's bid to return to the Champions League, with the result marking the clubs first win at The Hawthorns since 2011.
The Baggies now occupy eighth position in the Premier League table and are likely to finish in the top-half in the club's first season under new Chinese owner Guochuan Lai.
Liverpool's manager was particularly wary of the threat that West Brom might pose from set-pieces, an area in which his team have been vulnerable defensively this season.
The winger connected well with his shot but it was smothered low down by Mignolet.
But that didn't prevent them from nearly taking the lead midway through the first half.
Liverpool have won all eight away PL games before today in which Roberto Firmino has scored. The Brazilian's influence grew as the match wore on and would have had an assist if Milner hadn't blazed over.
West Brom were set up to keep a clean sheet, that Pulis so loves.
The goal completely changed the outlook of the match.
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In second-half stoppage time, West Brom sent goalkeeper Ben Foster up for a corner but Liverpool claimed possession. "He was really good, I have to say, really lively, and very important again". Liverpool, inspired by their late first half heroics, started very brightly.
Divock Origi had the ball in the back of the net but the goal was ruled out for offside, which was the correct call.
"I've just had a chat with him".
Georginio Wijnaldum slid a nicely weighted pass into Firmino's path and the goalscorer chipped across the West Brom box, where Milner charged forward from left-back to volley over. Subs: Morrison 6, McClean 6, Rondon 7.
Liverpool's defence stood firm impressively in front of goalkeeper Simon Mignolet, showing a resilience they have lacked at times this season.
The chance motivated the West Brom faithful, though, and Liverpool began to look nervy.
Mane joined Jurgen Klopp's revolution at Anfield from Southampton last summer for a reported £34m. I liked it a lot that in the second half we looked better tuned than the first half. Subs: Sturridge 6, Moreno n/a.
Much to the relief of Alberto Moreno, though, the Reds held on to secure another huge win in their top four fight.
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