Ramires and Victor Moses were on target as Rafa Benitez's men overcame Tony Mowbray's Championship side at the Riverside, setting up a last-eight tie with the Red Devils
The hosts managed to hold the Blues until half-time but could do nothing about Ramires' deflected effort which gave the visitors the lead on the hour mark.
Victor Moses made sure of Chelsea's progress with his sixth goal of the season midway through the second half.
Rafa Benitez made eight changes from the defeat to Manchester City last time out. John Terry returned in defence, while Yossi Benayoun made his first start in over two years and Nathan Ake made his full debut for the Blues in midfield.
Tony Mowbray, meanwhile, made three changes to the side which lost 2-1 at home to Millwall on Saturday, with Mustapha Carayol, Faris Haroun and Scott McDonald coming in.
A packed Riverside Stadium saw the hosts get off to a shakey start as Chelsea scuppered a number of early chances.
Paulo Ferreira was inches away from getting on the end of a cross from Oscar at the far post before Fernando Torres fizzed another fine pass across the Boro box with no team-mate there to meet it.
The hosts survived another scare moments later when Victor Moses picked out Oscar in the box after a powerful run, but the Brazilian's first-time finish was well blocked by Jason Steele.
But Mowbray's side managed to get back into the tie midway through the first half with the help of the home support. McDonald wasted a glorious chance when he headed inches wide of the post after meeting Nicky Bailey's cross in the 26th minute.
Boro continued to grow into the game and almost had another chance when Petr Cech spilled Mustapha Carayol's long range shot five minutes before the break, but Terry reacted first to clear the danger.
Benitez would have had some stern words for his players at the break as their bright start quickly dissipated, allowing the hosts to gain the impetus.
Chelsea came out for the second half with visible intent and they were immediately rewarded as Ramires curled home a right-footed shot from the edge of the area which took a deflection off Torres on its way into the top corner, just six minutes after the break.
The visitors could have doubled their lead on the hour but Torres' shot whistled over the bar after he managed to beat Boro's offside trap.
The game was eventually wrapped up in the 72nd minute when Oscar and substitute Eden Hazard picked apart the Boro defence, before Moses capped off a fine move with an easy tap in from close range. The Belgian had transformed the game after coming on from the bench.
Oscar wasted a chance to get Chelsea's third and Middlesbrough came close through Seb Hines in the closing stages.
Another chance went begging for Boro when Miller sliced his left-footed shot into the side netting at the death, but at that point the visitors progress into the sixth-round was already secure.