First-half goals from Romelu Lukaku and Hakim Ziyech took Chelsea into the semi-finals of the FA Cup.
Championship side Middlesbrough caused them some problems but the Blues went ahead when Mason Mount collected Ziyech’s ball down the right and crossed low for Lukaku to score from close range.
And Ziyech doubled the lead by cutting in from the right and firing a left-footed shot past Joe Lumley.
After the interval, former QPR keeper Lumley kept out Timo Werner’s header from Mount’s left-wing cross.
Werner was also denied by Sol Bamba’s block as Chelsea threatened to add a third.
Chelsea: Mendy, Azpilicueta, Silva, Rudiger, Sarr, Kovacic (Kante 69), Loftus-Cheek, Mount, Ziyech (Kenedy 81), Lukaku (Vale 84), Pulisic (Werner 68).
Subs not used: Bettinelli, Alonso, Chalobah, Barkley, Havertz.