Spurs manager Jose Mourinho made five changes from the thumping win over Leeds United, with Serge Aurier, Davinson Sanchez, Sergio Reguilon, Moussa Sissoko and Lucas Moura returning to the line-up.
The hosts had a bright start after Sissoko sent got the opening goal in the 13th minute with a free header inside the box after a delightful cross by Reguilon.
The Bees offered much better resistance after that, as Ivan Toney had their first chance to equalise ten minutes before the break but his glancing header was gathered by shot-stopper Hugo Lloris.
Toney nearly scored an own goal four minutes later after contesting a cross from a corner with Moura, but goalkeeper David Raya Martin made a great reflex save to keep Brentford in the game heading to the break.
Chances were falling for both sides early in the second stanza but Aurier should have made it 2-0 for the hosts six minutes after the break after pouncing on a loose ball at the near post but he guided his shot over the top corner.
Thomas Frank's troops thought they had equalised on 65 minutes after Toney headed in from close range a headed cross from Ethan Pinnock but the goal was disallowed for offside by the Video Assistant Referee (VAR).
However, Son eventually doubled Spurs' lead in the last 20 minutes with thumping a looping shot past Raya Martin after latching onto a through ball by Tanguy Ndombele.
Brentford's slim chances of a comeback evaporated in the last seven minutes after Josh Dasilva was shown a red card for a lunging tackle on Pierre-Emile Hojbjerg, who had to be substitute off.
In the end, Mourinho's men comfortably clinched a 2-0 win and they will now await the winner of the second semi-final between Manchester United and Manchester City on Wednesday.