Erikson opened the scoring after 11 minutes.
Collecting Lamela's pass, he was given time at the edge of the Swansea penalty area. His left foot shot arced into the top right hand corner past Swansea goalkeeper Kristoffer Nordfeldt.
Lamela effectively ended the contest on the stroke of half-time. The Argentine jinked his way into the area and fired the ball past Nordfeldt.
Eriksen was set up for his second by the former Paris Saint-Germain striker Lucas Moura.
Last year Tottenham lost in the semi-final to Chelsea.
A rematch is possible as the west Londonders face Leicester City on Sunday.
In the other quarter-finals, Manchester United host Brighton and Hove Albion and Wigan Athletic entertain Southampton.