Sandro Tonali's sweet strike, the Italian's first goal since August 2023, fired the hosts ahead in the opening stages of the quarter-final tie before the midfielder's equally impressive volley from Anthony Gordon's corner extended United's advantage before the half-time whistle.
Fabian Schär's close-range finish added further gloss to the scoreline in the second-half before Yoane Wissa's stoppage-time effort proved a mere consolation as Eddie Howe's side secured a last-four spot in the competition for a second time in their last three seasons.
After a convincing 4-0 win against Leicester City last weekend, Howe named an unchanged starting XI to face the Bees, who claimed a 4-2 victory against the Magpies in the Premier League eleven days ago.
Shooting towards the Leazes End in the first-half, Newcastle made a bright start as Joelinton latched onto Jacob Murphy's low cross from the byline before the Brazilian's drilled effort inside the box was blocked by Bees defender Nathan Collins.
In the ninth minute, Tonali sent United ahead in splendid fashion. After Tino Livramento completed a darting run into the penalty area before the right-back's low cross was half-cleared by Collins into the central midfielder's path, who lashed a wonderful first-time effort from the edge of the box into the net.
Anthony Gordon was unable to double the Magpies' advantage as the Liverpool-born winger raced onto Schär's quickly taken free-kick from distance but after electing to shoot inside the penalty area, fired his attempt wide of the target.
Tonali doubled his and United's goalscoring tally in the 43rd minute as the 24-year-old connected with Gordon's lofted corner from the right flank before powering a fierce volley beyond Brentford goalkeeper Mark Flekken.
Murphy, who scored a brace in United's 4-0 win against Leicester on Saturday, was unfortunate not to extend Newcastle's lead further on the stroke of half-time. After Bruno Guimarães and Tonali almost combined neatly in attack, the latter found Alexander Isak who teed up Murphy inside the box before the in-form winger placed a firm effort against the right-hand post.
Joe Willock, introduced from the substitutes' bench at the the restart, went close to netting United's third of the night after completing a darting run into the penalty area before the midfielder's shot at goal was blocked out for a corner by Brentford defender Ben Mee.
Gordon took his turn in front of goal minutes later after dangerously advancing into the penalty area before the 23-year-old's bending effort flew narrowly wide of the far right-hand post.
Murphy went agonisingly close to netting his third goal of the 2024/25 season after combining with Guimarães on the edge of the box, who played a neat back heel into the former's path before his resulting effort curled inches past the left-hand post.
United goalkeeper Martin Dúbravka produced a key stop to prevent Keane Lewis-Potter from halving the deficit after the Bees winger evaded Livramento's sliding tackle inside the box before his drilled strike was beaten away by the Slovakia international.
In the 69th minute, Schär grabbed Newcastle's third goal of the night. After Lewis Hall's initial strike was parried by Flekken, the unselfish Guimarães cleverly dragged the ball into the Swiss defender's path, who stroked the ball into the net inside the six-yard area.
Tonali went close to netting a hat-trick in the closing stages of the cup tie after Guimarães' corner was only cleared into the midfielder's path who saw a fizzing shot blocked out for a corner inside a crowded box.
Barnes was unfortunate not to grab his third goal in as many matches against Brentford as the 27-year-old collected Willock's pass before firing a fierce effort off the foot of the left-hand post.
Newcastle's hopes of back-to-back clean sheets were dashed in the first of three stoppage-time minutes as Wissa scored for the visitors, firing home from Bryan Mbuemo's pass inside the penalty area but the goal would not prove costly for the Magpies as they booked their place in Thursday's semi-final draw, which will take place after the conclusion of Tottenham Hotspur's last-eight tie against Manchester United tomorrow night.
Newcastle United: Martin Dúbravka, Fabian Schär, Joelinton (Joe Willock 46), Sandro Tonali, Anthony Gordon (Miguel Almirón 77), Alexander Isak (Will Osula 77), Lewis Hall (Kieran Trippier 77), Tino Livramento, Jacob Murphy (Harvey Barnes 65), Dan Burn, Bruno Guimarães (c).
Substitutes: Odysseas Vlachodimos, Matt Targett, Lloyd Kelly, Lewis Miley.
