Brentford were unable to pull off the sensational win it would take taken for them to reach the Carabao Cup final.
They can consider themselves unfortunate after being denied an equaliser when Ivan Toney had a goal disallowed after VAR showed the striker was marginally offside.
Goals from Moussa Sissoko and Son Heung-min were enough to see off the Bees, who played the final six minutes with 10 men after Josh Dasilva was sent off.
Spurs took control when Sissoko headed home Sergio Reguilón’s left-wing cross after 12 minutes.
Brentford, in the club’s first-ever major semi-final, were always competitive and Spurs breathed a sigh of relief after Toney nodded in from close range only for the goal to be chalked off.
The hosts’ victory was sealed when Son latched onto Tanguy Ndombele’s pass and fired home.
Dasilva was red-carded for a crude challenge on Pierre Hojberg.
Brentford: Raya, Dalsgaard, Sorensen, Pinnock, Henry, Dasilva, Janelt (Emiliano 74), Jensen, Mbeumo (Forss 81), Toney, Canos (Fosu 74).
Subs not used: Daniels Ghoddos, Roerslev, Stevens, Gilbert, Haygarth.