The London outfit, whose last appearance in the last four was during the 2008-09 season, took the lead after 18 minutes at White Hart Lane – Nabil Bentaleb breaking the deadlock with his first senior goal for the club.
Newcastle were largely restricted to speculative shots from distance, and any hopes of a bright start to the second half were dashed when Nacer Chadli doubled the advantage less than a minute after the interval.
Harry Kane's third after 65 minutes had home fans dreaming of a Wembley final, and Roberto Soldado's fourth five minutes later only served to compound the visitors' misery.
The result sees Tottenham atone for a 2-1 home defeat to Newcastle in the Premier League in October, and replicates the 4-0 scoreline they achieved on their last visit to St James' Park.
Mauricio Pochettino elected to make six changes from Sunday's 2-1 Premier League victory over Swansea City – Michel Vorm among the players to come in – while Alan Pardew, who made four alterations, will have been envious of Tottenham's strength in depth between the posts, as he stuck with Jak Alnwick in the absence of injured duo Tim Krul and Rob Elliot.
It was Tottenham who applied the early pressure and, although Moussa Sissoko tested Vorm with a long-range strike, the hosts soon exposed Newcastle's goalkeeping frailties.
Alnwick failed to collect a corner whipped in from the left, pushing the ball over his head and into the path of Bentaleb, who showed great reactions to prod home an 18th-minute opener.
Kane, who opened the scoring in the win over Swansea at the weekend, picked up a loose pass in midfield after 35 minutes, but his eventual effort whistled wide of the left-hand post when he pulled the trigger from 20 yards.
Kane went down in the box under the challenge of Newcastle captain Fabricio Coloccini shortly before the interval. There was certainly contact, but referee Andre Marriner opted against pointing to the spot.
Marriner was equally unconvinced when Ayoze Perez was challenged by Danny Rose at the other end.
Pardew had his players out early doing extra warm-ups before the start of the second half, but it failed to have the desired effect as Chadli drifted in from the left wing to fire a low effort beyond Alnwick from 20 yards within a minute of the restart.
Newcastle should have reduced the deficit soon after when Perez's ball across the six-yard box evaded both Remy Cabella and Emmanuel Riviere, but Tottenham continued to push for a third.
Alnwick had to be alert to keep out a low drive from Vlad Chiriches shortly before the half-hour mark, before Paul Dummett sent the ball just over his own crossbar and a Jan Vertonghen header was cleared off the line by Sissoko.
The third goal finally arrived in the 65th minute when Kane latched onto an Andros Townsend throughball to fire beyond Alnwick, and substitute Soldado completed the rout when he reacted quickest to a parry to find the net within a minute of coming on for Kane.
Alnwick caused concern when he received treatment for a shoulder problem shortly after conceding the fourth, but was on hand to keep out Soldado when the Spaniard had a shot from close range.
Pochettino's men are now just one step from the final in March, while Pardew, who twice saw 17-year-old Adam Armstrong go close to snatching a consolation goal late on, will be keen to erase this result from his players' memories ahead of Sunday's derby clash with Sunderland.
