Goals from Romelu Lukaku and birthday boy Hakim Ziyech gave the visitors a straight forward win at the Riverside stadium.
For the hosts, it’s sadly the end of the road and the possibility of securing a hat trick of upsets proved to be too difficult of a task.
In previous rounds Chris Wilder’s side shocked Manchester United and Tottenham, beating United on penalties, before securing an impressive 1-0 win over Spurs.
Whilst in no way did they embarrass themselves in front of a packed out crowd, Chelsea’s class was telling, particularly with their goals.
The first, a fine counter-attack after Hakim Ziyech played a ball down the line to Mason Mount who then produced a low ball into the six yard box for Romelu Lukaku to tap in.
There was no question in the quality of the goal, but commentating on the match for talkSPORT, Trevor Sinclair thinks Boro’s high defensive line didn’t help.
“That’s exactly what can happen, it was a high line from Middlesbrough, excellent ball from Mount and it’s a tap in for Lukaku,” he said.