Berahino stepped up to score with four minutes remaining on a wet and blustery afternoon at The Hawthorns after Newcastle goalkeeper Tim Krul brought down Matej Vydra.
Krul escaped a red card for his challenge but team-mate Mathieu Debuchy saw no such leniency from referee Lee Mason after a two-footed challenge on Claudio Yacob.
It was West Brom's first victory in 10 games and was thoroughly merited after a hard-working performance.
It lifted some of the gloom with which 2013 ended after the sacking of head coach Steve Clarke and put aside the controversy generated by Nicolas Anelka's goal celebration last weekend.
Anelka could have done some of that himself had he not scooped over from close range before the break while Liam Ridgewell also missed a fine opportunity.
The Baggies forced the pace in the second half but what creativity there was in a largely subdued first period was created by the hosts.
Newcastle's Loic Remy fired over with the first serious attempt of the game but the impressive Morgan Amalfitano was the first to test a goalkeeper when he shot straight at Krul.
An ambitious attempt by Amalfitano to lob Krul from the right was dealt with by the goalkeeper before the same player shot over.
West Brom continued to look the livelier and Stephane Sessegnon was inches away from turning in a Ridgewell cross after good work by Anelka.
Baggies defender Billy Jones required treatment for a head injury after colliding with his own goalkeeper Ben Foster. The pair had both been forced to change direction and stretch for the ball after a Remy shot had taken a looping deflection.
That proved a rare attack from Newcastle and Jonas Olsson went close at the other end when he headed wide from an Amalfitano cross.
Amalfitano made more headway down the right and pulled back a good cross for Chris Brunt but the Albion captain, despite having time to aim from 10 yards, could not get direction on his header.
Anelka spurned an even better opportunity just before half-time, after yet more trickery from Amalfitano, when he remarkably shot over from four yards.
Jones did not return for the second half as Downing decided to liven up the attack by sending on Berahino.
Cheick Tiote tried his luck from distance for Newcastle after a clearance fell his way but Foster was alert to his bobbling volley.
West Brom decided to try a few long-ball attacks and one of them almost paid off as Berahino lashed in a shot after combining with Brunt but a defender blocked.
The tempo of the game started to increase as Remy controlled outside the area and cut inside to curl a shot over Foster's bar.
Newcastle were left facing an uphill struggle after Debuchy was dismissed in the game's first moment of controversy just after the hour.
Mason had no hesitation in showing a straight red card after Debuchy lunged in on Yacob, even though the Argentinian managed to jump and minimise contact.
Albion grew in confidence after that and forced the pace even more.
Newcastle regrouped and repelled a succession of attacks with Krul not seriously tested until Berahino fired a shot low at his near post after 75 minutes.
Yohan Cabaye - who Newcastle fans made clear they do not want to leave as they contemplated a month of transfer speculation - needed treatment after a challenge by Amalfitano but played on.
Ridgewell spurned a glorious opportunity nine minutes from time when he reached a Berahino cross ahead of Krul four yards out but somehow sidefooted wide.
There was still time for West Brom and their chance came after Vydra raced through and was tripped by Krul.
Berahino made no mistake and Newcastle could not recover, despite Cabaye shooting at Foster.