Rafa Benitez made a host of changes with captian John Terry returning, whilst the likes of Yossi Benayoun, Victor Moses, Paulo Ferreira and debutant Nathan Ake also started for the European champions in their fifth round tie.
Both goals arrived in the second half, as Chelsea ran out deserved winners. The first came just after the break when Fernando Torres managed to get in the way of a Ramires half-volley from the edge of the box and the deflection took it past the helpless Jason Steele.
The win was sealed with 17 minutes left as Moses poked the ball home from close range.
Boro had huffed and puffed in the latter stages, but they failed to trouble Petr Cech, as Chelsea progressed and avoided Rafa Benitez's feared replay, which would have added an extra game to their hectic schedule.
Chelsea had started brightly with Oscar seeing plenty of the ball and he created the first opening seven minutes in with a lovely ball into the six-yard box but neither Ramires or Benayoun could react.
Torres then flashed a similar ball across goal with again nobody in place to convert. Moses impressed down the right, but Steele did not have a save to make in the opening period.
It was Boro on the counter-attack who gave Cech more to think about. Just before the half-hour Scott McDonald flashed a header wide after an excellent ball in from Nicky Bailey.
Then the Czech Republic international was a relieved man just before the break as he failed to deal with a Muzzy Carayol drive which bounced up in front of him and off his chest, but fortunately it deflected to Terry and Chelsea cleared their lines.
In the second period Chelsea suddenly turned up the pressure gauge and penned Boro into their own half before breaking the deadlock just minutes in.
Oscar broke on the right, worked his way into the box and crossed to the back post. The chance looked to have gone with Benayoun helping it to the edge of the box, but Ramires was there to fire at goal and the ball beat Steele courtesy of a deflection off Torres.
Straight from kick-off, Chelsea wasted another good chance as Moses broke into the box and fired a cross-shot into the six-yard box but there was nobody backing him up.
Boro brought on Ishmael Miller for the last 20 minutes, but with Terry and co rarely looking troubled Chelsea continued to push and claimed a second as Moses poked the ball home from close range as they sealed their place in the quarter-finals.