Miguel Almiron opened the scoring for the Steve Bruce's men just after the half-hour mark before going onto claim his fourth goal of the competition in first-half stoppage.
It was then a minute after the break when Newcastle United added a third through the January signing Valentino Lazaro which proved to be the winner.
West Bromwich Albion rallied though and got their reward following a period of pressure through a Matt Phillips strike and then in added-on time through Kenneth Zahore.
Story of the game
It was a vibrant start to the cup clash between two sides whose league campaigns are essentially taking priority, but tonight proved a welcome distraction for Newcastle.
Almiron was almost played through on goal inside just four minutes but after advancing forward, Nabil Bentaleb misplaced his delivery and the former couldn't latch on.
The hosts responded instantly, however, when wide-man Kyle Edwards unleashed a firm strike but Karl Darlow was on hand to beat the ball away.
Newcastle were the next to go close when Allan Saint-Maximin unleashed a swerving pile-driver from 25 yards which struck the wrong side of the post and out to safety.
Slightly rejuvenated from playing in his natural position on Saturday, Joelinton was looking a threat in the final third and did excellently in the 19th minute to cut in and let fly - but his shot was deflected behind.
Almiron showing his worth
In the 32nd minute though, the deadlock was broken when Almiron collected a delightful through ball from Saint-Maximin before composing himself and calmly slotting home.
The Paraguayan international then doubled the Magpies' lead in added on time of the first half, lashing the ball home with his left-foot following a neat Joelinton back-heel.
If conceding with the last action of the first half was a blow to Slaven Bilic's men, what happened after a minute of the second period will have been even worse when Lazaro added the third.
The Austrian announced himself to the Geordie faithful when he bundled home from close range to ease Newcastle nerves, who surrendered a two-goal lead in the previous round at Oxford United.
Hosts finally stepped up
It took until they were three-nil down for Albion to begin playing their best football.
Newcastle had Danny Rose to thank in the 51st minute when he backtracked to divert the ball off the line, following Matt Phillip's chip over Darlow.
Then, on the hour mark, it was Phillips again who came close as he almost converted a rapid ball across the six-yard box.
It was then the turn of the Baggies to see the woodwork hit when Edwards' shot from the distance came back of the bar via a deflection from Jamaal Lascelles.
The pressure finally did pay off, when Newcastle failed to clear their lines and Phillips did make amends from his earlier opportunities, hammering home inside the area.
With the final ten minutes to play a familiar face in the West Midlands re-appeared in the form of Dwight Gayle, who netted 24 times last season for the club.
The game was gradually slipping away from the hosts, but on 85 minutes Fabian Schar was needed to hook another ball off the line.
Schar was then involved at the other end when a fierce strike was saved by Jonathan Bond.
It was to be another nervy final minute for the five thousand-strong United following when substitute Kenneth Zohore tapped home, but ultimately it was left too late for a comeback.
Newcastle had gone three league matches in a row without a goal, but tonight proved they do have the attacking minerals in them. Yes against a Championship side, but top of their division and it's likely they will meet again in the Premier League soon enough.
West Brom showed enough spirit second half that has ultimately helped them to the top of the table. A starting eleven sprayed with changes, they still caused United danger and certainly on another night things could have been different if they converted their chances.
Man of the Match
It's hard to dispute a two-goal contribution for his side, and in truth, Almiron was everywhere on the field. His first goal radiated class and his second gave Newcastle a better cushion going into the second period. A real threat when it is his day.