N’Golo Kante’s precise 51st minute strike was enough for Conte’s team to break United’s hold on the Cup after the visitors had Ander Herrera sent off after 35 minutes for a second yellow card, both for fouls on Eden Hazard.
Premier League leaders’ Chelsea’s reward is a Wembley clash with Tottenham Hotspur next month, while the other semi-final will be between Arsenal and Manchester City.
United, who face a Europa League last 16 tie on Thursday against Russian side Rostov, were missing the suspended Zlatan Ibrahimovic and injured Wayne Rooney and offered little threat once Kante had beaten David de Gea with a precise low shot.
Mourinho was spared the humiliation of the 4-0 thrashing his old club dished out in October’s league meeting -- his first return to Stamford Bridge since being sacked last season -- but his United side were again found wanting.
Mourinho’s frustration boiled over at times and the Portuguese and Italian Conte had to be separated after an angry exchange shortly after Herrera’s sending off.
“The game was completely under control (before the red card),” Mourinho, whose players targeted Hazard for especially close attention, told reporters. “They couldn’t find what is their game. I cannot be more proud of the players.”
Chelsea, chasing the Premier League/FA Cup double they last achieved in 2010, dominated possession and could have scored more goals, though holders United had their moments.
