Goals from Reece Mitchell and Kasey Palmer, plus a spectacular strike from the half-way line by Ola Aina, saw the Blues surge into a three-goal lead inside 35 minutes at the Lamex Stadium.
We responded in the second half through Anton Walkes and Will Miller, but a late brace from Tammy Abraham sealed Chelsea's progress into the last four.
Spurs U21s: Glover, Walker-Peters, J Pritchard (Oduwa 74), Lesniak (Goddard 63), Maghoma, Veljkovic (c), Sonupe, Amos, Miller, Walkes, Georgiou. Substitutes (not used): Paul, Voss (GK).
Chelsea U21s: Collins, Dabo (c), Aina, Clarke-Salter, Wright, Houghton (Sammut 75), Wakefield (Conroy 80), Quintero (Scott 69), Abraham, Palmer, Mitchell. Substitutes (not used): Ugbo, DaSilva, Baxter (GK).
Above: Milos Veljkovic in an aerial challenge with Jake Clarke-Salter.