The result left Newcastle four points above the drop zone in 16th place on 27 from as many games, while West Brom stayed second-bottom on 18 from 28, eight points from the safety area.
Newcastle had the upper hand in the opening 15 minutes as they staged several fast breaks and only a superb clearance by Darnell Furlong from a Joelinton cross denied Ryan Fraser a close-range tap in.
The hosts then spurned a pair of sitters either side of halftime as Newcastle goalkeeper Martin Dubravka tipped away Mbaye Diagne's header before Matthew Phillips blazed a shot over the bar from eight metres.
West Brom's Johnstone then turned a Joseph Willock shot around the post on the hour before the pace dropped in the closing stages, with Newcastle holding out comfortably as West Brom applied some late pressure.
West Brom's defiant boss Sam Allardyce urged his team to keep battling as he praised their newly-found defensive grit, although he conceded they lacked edge up front.
"The players need to keep their chins up and play like they are playing," he told the BBC. "The only thing missing is converting the chances we create. We have got the defensive side of it spot on now.
"The players have to keep doing what they are doing and try and be determined enough to try and change the scoreline themselves by putting the ball in the back of the net.
"We certainly had enough chances to accumulate 12 points in the last few games and not just four."
Visiting under-pressure manager Steve Bruce was confident his side would stay in the top flight.
"Eleven games to go, we've done OK," he said. "The last five or six games there's only been Chelsea and Manchester United that have beaten us. We will take a point and move on.
"I was delighted with their attitude and spirit. We showed a real desire to get something out of the game. In terms of the problems we've had, it was important."