Fabian Schär fired the hosts ahead at St. James' Park, heading the ball home from Sandro Tonali's inviting corner, before Nick Woltemade's header shortly after the restart doubled the Magpies' lead.
The Magpies then saw out the cup tie to record a third successive win across all competitions as well as securing an eighth clean sheet of the 2025/26 season in the process, and maintain the defence of their Carabao Cup crown.
Eddie Howe made eight changes from Saturday's 2-1 victory against Fulham, with only Woltemade, Malick Thiaw and Dan Burn retaining their places from last weekend's last-gasp win against the Cottagers.
United, targeting a fourth consecutive Carabao Cup quarter-final, began the cup contest in positive fashion as Thiaw went close to netting his first goal for the club since his summer move from AC Milan, with the German's close-range header from Sandro Tonali's free-kick parried by Antonín Kinský before Joe Willock saw a first-time shot at goal blocked by João Palhinha.
Jacob Ramsey, also targeting a maiden strike for the Magpies after joining the club from Aston Villa last summer, took his turn in front of goal after latching onto Dan Burn's dangerous pass but saw his powerful drive blocked by Spurs skipper Pedro Porro.
Thiaw produced a crucial last-ditch challenge to prevent Richarlison from firing an attempt at goal, with the 24-year-old centre-back tracking the Brazilian's run towards goal before blocking the effort out for a throw-in to the delight of the home crowd.
Newcastle, targeting a fourth win in a row against Tottenham, took the lead in the 24th minute courtesy of Schär as the Swiss defender rose high from Tonali's teasing corner before guiding a firm header beyond Kinský.
The hosts preserved their one-goal cushion shortly after despite Spurs going close to levelling the cup tie, with Richarlison failing to connect with Lucas Bergvall's teasing pass across the penalty area before the Spurs forward, minutes later, failed to place the ball into the net from Brennan Johnson's cross-cum shot.
Barnes struck the crossbar for the hosts before half-time as the left winger latched onto Thiaw's intended shot at goal following Tonali's dangerous cross into the box, before his acrobatic volley thundered onto the woodwork.
Newcastle extended their advantage in the 50th minute as Woltemade netted his sixth goal of the season across all competitions. After Thiaw regained possession before finding Willock, the latter lofted a delightful cross into the German's path who beat Kinsk ý to the lofted ball before heading into an empty net.
Aaron Ramsdale, who made his competitive Magpies bow in last month's 4-1 win against Bradford City, produced an excellent stop to prevent Pape Matar Sarr from halving the deficit, blocking the Senegalese midfielder's powerful strike at goal with his left arm before Porro's cross from the byline was crucially turned out for a corner by Schär.
The 27-year-old goalkeeper was alert once again after producing an unorthodox save to deny Richarlison, with the Brazilian's effort from Porro's dangerous cross striking his body before the loose ball was cleared to safety.
Newcastle almost netted a third in the closing stages as Schär's wonderful curling cross was met by Anthony Elanga at the back post before his intended pass to substitute William Osula struck Kevin Danso's head before flying inches wide of the right-hand post.
The full-time whistle was met by a rapturous applause as the hosts sealed a fourth win in a row at St. James' Park, with hopes of a third trip to Wembley Stadium in the last four campaigns remaining on course.
Newcastle United: Aaron Ramsdale, Fabian Schär, Sandro Tonali, Harvey Barnes, Malick Thiaw, Emil Krafth (Kieran Trippier 71), Anthony Elanga (Anthony Gordon 89), Nick Woltemade (William Osula 71), Joe Willock (Joelinton 71), Dan Burn (c), Jacob Ramsey (Bruno Guimarães 79).
