Eriksen accepted the freedom of the Liberty Stadium given to him by Swansea to score his seventh and eighth goals against the Welsh club in 10 matches - one would have thought they would have learned their lesson by now - and Érik Lamela effortlessly stroked home Tottenham's second.
The victory raised Tottenham's hopes of a first trophy since they won the League Cup in 2008.
Their absence will be greatly felt especially Jordan, whose two goals in the competition has contributed to Swansea reaching this stage for the first time in 54 years.
Seven straight wins at the Liberty Stadium were soon forgotten as Spurs established a real control on proceedings.
After the Swans' impressive form in the Premier League of late, to see them outplayed on their own turf was cause of concern for the home crowd, but Spurs were clearly enjoying their football and it was more of a case of the visitors being too good on the day.
Spurs were without Harry Kane for the game as the England striker begins a spell on the sidelines with damaged ankle ligaments, however, they did not miss his presence in this particular fixture.
Spurs immediately appealed for the decision to be reviewed and despite replays seemingly showing Son to be level, the original verdict was upheld after a lengthy delay. Jurgen Klopp has few options other than his forward line of three, though when Mo Salah, Sadio Mane and Roberto Firmino are as effective as they are, against all types of defences, then only a major injury crisis would prompt a re-think.
Spurs continued to dominate possession and, with Lucas Moura offering pace and trickery on the right, Lamela zipping about with goal and Eriksen pulling strings, every time they went forward Spurs looked like they had real intent about them.
Tottenham's second-choice keeper Michel Vorm, formerly of Swansea, had little to do although he made one great double save just after the break, stopping Martin Olsson's piledriver before reacting well to save Abraham's headed follow-up.
Just past the hour, Spurs sealed the victory. Seven months ago it was horrendous to play there and now it's an advantage.