Swansea started brightly as they targeted a first appearance in the last four of this competition since 1964, but it did not take long for Spurs to find their rhythm and the visitors opened the scoring in some style.
After receiving the ball from Lamela, Eriksen was allowed to move towards the penalty area before curling a delightful effort into the far corner from 20 yards out.
Midway through the first half, Son Heung-min had the ball in the net after collecting a high ball before finding the underside of the crossbar with his half-volley, but his goal was harshly ruled out by a combination of the assistant and VAR.
Swansea were offering very little in the final third and as half time approached, Spurs began to up the tempo with Eriksen seeing another long-range strike tipped onto the crossbar by Nordfeldt.
Eric Dier also squandered a headed chance for the visitors but in added-on time, Spurs doubled their lead when Lamela was given the space to curl a low 20-yard strike into the bottom corner.
Carlos Carvalhal introduced Luciano Narsingh at half time and within a minute of the restart, Swansea had almost halved the deficit with Martin Olsson seeing a 20-yard strike parried by Michel Vorm before the goalkeeper got back to his feet to keep out Tammy Abraham's header.
Spurs responded through Dier, who watched Nordfeldt somehow manage to prevent his 30-yard attempt from finding the top corner, but the visitors did not have to wait long for their third.
Dier and Moura combined before Eriksen was teed up on the edge of the area, and the midfielder managed to drill the ball through a number of defenders to beat Nordfeldt from 20 yards.
Eriksen soon set about trying to complete his hat-trick but from almost an identical position for his second goal, his attempt was comfortably saved by Nordfeldt.
The final quarter of the match was played at a lower tempo, but Mauricio Pochettino still opted to introduce Dele Alli for a cameo appearance while keeping the much-used Eriksen and Alli on the pitch.
Former Swansea forward Fernando Llorente squandered two close-range openings for Spurs after being brought on a substitute but it mattered little as Spurs comfortably sealed their place in the semi-finals of this competition for the second successive year.
SWANSEA CITY (5-4-1): Nordfeldt; Naughton (Narsingh (46'), Van Der Hoorn (Roberts 81'), Mawson, Bartley, Olsson; Dyer (Routledge 86'), Ki, Carroll, Clucas; Abraham
TOTTENHAM HOTSPUR (4-2-3-1): Vorm; Trippier, Sanchez, Vertonghen, Davies; Dier, Sissoko; Lamela (Alli 81'), Eriksen, Lucas (Llorente 73'); Son