Ben Foster had to pull off a stunning save to deny Dwight Gayle an equaliser seconds before the break, but was otherwise largely untroubled.
At St James' Park, the Baggies showed the sort of gutsy performance their opponents had shown in recent weeks.
Survival will still be a big ask, with Albion still five points from safety with only two games to go.
Matt Ritchie has scored in three of his last four Premier League home games, having failed to find the net in his previous 12 top-flight matches at St James' Park this season.
The Magpies were very almost level when Kenedy played a neat one-two with Ayoze Perez and saw his stabbed effort graze the foot of the post with Foster beaten and Gayle awaiting a square ball, although overall, their response was tepid until the dying seconds of the half.
Game 1: Bruins leads Lightning 2-1
Rick Nash got his blade on the puck and redirected it between Vasilevskiy's pads for his second power-play goal of the playoffs. One thing about the playoffs is that you can blow a 3-1 lead, win a Game 7 and pretend like nearly nothing dramatic happened.
Rafael Benitez's side came close again in the final minutes of the first half, but Gayle's header was brilliantly kept out by Foster, who clawed the ball off the line to ensure the visitors maintained their advantage.
Newcastle United substitutes: Darlow, Clark, Manquillo, Hayden, Murphy, Joselu. I congratulate the players for a good season, but we need to be better than today.
Phillips' goal was his first in 22 games in all competitions for West Brom, since netting against Manchester City in October.
Newcastle United fans were left tearing senior midfielder Jonjo Shelvey to shreds on social media after his performance in the 1-0 defeat against West Brom on Saturday.
There were 15 shots in total in the second half in this game (10 for Newcastle, five for West Brom), but none were on target.