In the event, they did make the journey to the north-east by air amid uncertainty regarding their travel arrangements following sanctions imposed on owner Roman Abramovich by the UK Government.
They then proceeded to breeze into the semi-finals as Yorkshire’s wait for a first semi-final appearance since 2014 continued with Boro’s own wait going back further to 2006.
On the back of shocks against Manchester United and Spurs and given the fact that Chris Wilder’s side had won their last nine home fixtures at an expectant Riverside, there was hope of more theatre.
Chelsea, as all good sides do, spoiled the fun. They controlled the game following first half goals from Romelu Lukaku and Hakim Ziyech and despite a few flurries from the hosts, they were never in any serious discomfort.
Boro may be out, but their main concern is the Championship play-off race and the sight of Paddy McNair hobbling off early in the second half was a worry.
Chelsea made five changes, but at no cost in terms of their quality and wherewithal whatsoever. Quite the opposite in fact and their approach in the first half was businesslike and impressive.
Thomas Tuchel spoke about combating an ‘emotional crowd’ and his side did just that and silenced Teessiders in the process.
Their poise, first touch on the ball and thinking was much sharper and they struck where it mattered with Boro undressed on their left with two high-class counters yielding two goals.
A warning arrived early when Mason Mount’s low cross just failed to pick out Christian Pulisic at the back stick, but it was not heeded.
A break led by Ziyech, who had an eye-catching first half, soon found Mount, whose side split the Boro central defender with Lukaku getting ahead of Dael Fry to slot the ball home on 15 minutes.
It was a marker of Chelsea’s early intent, with Boro forced to hang in.
They did start to show more threat, certainly down the right where Isaiah Jones saw plenty of the ball and strived to make things happen.
Boro’s best moment came from a set-play with the unmarked Flo Balogun failing to get his header on target after Marcus Tavernier’s corner caught Chelsea dozing. Against sides like Chelsea, you simply have to take those sort of chances.
The Blues punished the hosts not long after with another fine counter.
It was started by Malang Sarr at the back, who found Mateo Kovacic, another to excel in the first period.
He slipped the ball to Mount, who promptly passed the ball to the dangerous Ziyech.
The winger was given too much space to cut inside by Neil Taylor before unleashing a swerving low shot which caught out Joe Lumley before nestling in the net.
The tie could have been well and truly over not long after following more piercing play by the visitors, with Anfernee Dijksteel doing well to clear off the line from Lukaku.
It was starting to look a game too far for Boro, who thankfully got to half-time with no further concessions.
Sol Bamba, with a brief to look after Lukaku, was brought on at the break, with Fry coming
Boro’s sell-out crowd needed something to feed off with the first chance of the half seeing Balogun fire over after a good break by the hosts.
Unfortunately, a second substitution, which saw McNair come off with injury, took any wind out of their sails.
Chelsea were quite happy to stroke the ball around, with one chance seeing Mount’s shot on the turn deflected wide.
For their part, Boro couldn’t grab the goal to turn the game into a proper cup tie again for the watching millions as well as the home fans present.
Another replacement in Duncan Watmore had a chance to do just that, but fired tamely over into the North Stand.
Fellow substitute Tino Werner had a chance to seal it, but headed straight at Lumley.
Boro’s hero in the previous round in Josh Coburn was soon thrown into the fray, but it was a night far different to the Spurs game and while Boro had some promising situations, their final ball just wasn’t there, despite the best efforts of Jones.
Bamba then denied the visitors a third after a great last-ditch block to thwart Werner.
Middlesbrough: Lumley; Dijksteel, McNair (Peltier 53), Fry (Bamba 45); Jones, Crooks, Howson, Tavernier, Taylor (Bola 58); Balogun (Coburn 73), Connolly (Watmore 58). Substitutes unused: Daniels, Hall, Olusanya, Boyd-Munce.
Chelsea: Mendy; Azpilicueta, Silva, Rudiger, Sarr; Kovacic (Kante 69), Loftus-Cheek; Ziyech (Kenedy 81), Mount, Pulisic (Werner 68); Lukaku (Vale 84). Substitutes unused: Bettinelli, Alonso, Chalobah, Barkley, Havertz.
Referee: P Tierney (Wigan).