The Blues won the trophy when the two faced each other in the 1997 final when Roberto Di Matteo scored a 30-yard screamer after just 42 seconds of play.
Since then, the fortunes of both clubs have changed dramatically with Chelsea tasting reaching the giddy heights of European glory whilst Middlesbrough have been absent from English football's top table since 2009.
The Blues failed to draw a save of any real note from Jason Steele in the first-half in what was a hotly contested 45 minutes of counter-attacking football. Boro had the best chance as Petr Cech was caught out by an awkward bounce, only for John Terry to appear to clear the danger.
The last thing Chelsea need is a replay as they have played twice a week, every week for three months, excepting the international break in January.
Whatever Rafa Benitez said at halftime worked, as a failed attempt at a volley from Yossi Benayoun fell kindly back to him, and he was able to lay it off to Ramires, who produced a strike of Brazilian quality to make it 1-0. The Israeli then made way for Eden Hazard, who played a lovely on-two with Oscar before squaring it to Victor Moses for a close range tap-in.
Middlesbrough rallied late on in the game, but a fine Petr Cech save from a Merouane Zemmama free-kick meant that the FA Cup holders progress to face Manchester United at Old Trafford in the quarterfinals.
Every player starts on 5/10 and points are awarded or deducted based on attitude, work-rate and contribution to the game. A goal scored by a defender is weighted higher than one scored by a striker and red cards and missed penalties get an automatic 1.0 deduction. Experience and form are taken into account.
Cech was very nearly caught out when a shot from Andre Bikey bounced awkwardly in front of him, and he saw a header from McDonald drift just wide of the post in the first half.
He had little to do for most of the second half, as Boro repeatedly failed to find the target, but he made a great save from a Merouane Zemmama to keep a clean sheet.
Paulo Ferreira has been Chelsea's forgotten man in recent years. Brought in by Jose Mourinho in 2004, Ferreira was the Blues' first choice right-back for several years while John Terry and Ricardo Carvalho dominated at centre-half. The arrival of Branislav Ivanovic saw him sidelined and he has been reduced to an occasional cameo appearance in the last three campaigns.
This was not his finest cameo and a pass to Branislav Ivanovic in the Chelsea box nearly released Scott McDonald, but considering his lack of competitive game-time it was a decent performance from the Portuguese.
Ivanovic began the game partnering Terry at centre-half and had a quiet first 45 minutes. He recovered well as a Paulo Ferreira pass nearly left him stranded, but otherwise he had little impact on the game.
Terry returned to the starting 11 having watched the Premier League defeat to Manchester City from the bench. His awareness was crucial to keeping the sides level going into halftime as he cleared his lines after a mistake by Petr Cech.
One of Terry's greatest strengths has always been his positioning, and he showed that off with aplomb in the second half, making several vital blocks to maintain Chelsea's lead. He has recovered well from the injury which saw him sidelined earlier in the season and should return to a regular starting role.
As the toils of playing twice a week begin to take their toll on the older players, Ryan Bertrand was called up to take Ashley Cole's place in the starting 11. He found himself running ahead of Yossi Benayoun on the overlap for most of the first half and found his man with two good crosses.
Bertrand put in a solid performance in the second half, and showed that another year under the tutelage of Cole should see him reach the same performance level as the current first-choice left-back.
Ramires moved back to the holding midfield role after a failed foray onto the right wing against Manchester City. His pace allowed him to track back and cover as Boro countered quickly in the first half.
Barely five minutes of the second half had elapsed before Ramires unleashed a fearsome shot from the edge of the box which flew into the top corner via Fernando Torres' shoulder. As the shot was on target before the deflection, he has been credited with the goal, and despite drifting out of the game for the final 10 minutes, his work-rate and effort were excellent.
Chelsea signed Nathan Ake from Feyenoord in 2010, and he entered the academy setup until being selected for the senior squad at the start of the 2012-13 season. The Dutch youngster plays primarily at centre-half, although he can be deployed as a defensive midfielder as Benitez chose to do for this fixture against Middlesbrough.
Ake did not set the tie alight in his first start, but he made some good tackles as well as some decent runs forward, a commendable achievement for the 18-year-old.
Victor Moses capitalised on the absence of Juan Mata and Eden Hazard from the starting 11 to make a case for himself starting on the right wing. A traditional winger, his pace and tenacity out wide caused all sorts of problems for Boro in the first half, and he won three corners for the team.
Hazard's introduction at the expense of Yossi Benayoun led to a beautifully worked goal which all of the attacking midfield trio played a part in. A one-two between Oscar and Hazard drew the defenders out wide, leaving plenty of space for Moses to make a well-timed run into the box to get the tap-in.
Moses was substituted a few minutes later, but he had already given Benitez plenty to chew on ahead of the EPL match with West Bromwich Albion at the weekend.
After a lacklustre performance at Manchester City, Oscar was the only of the Three Amigos to start the game against Middlesbrough. Taking Juan Mata's spot down the middle of the attacking three, Oscar received a lovely pass from Ramires on the edge of the 12-yard box, only to see his shot saved by Jason Steele.
The 21-year-old was involved in the build-up play for the second goal before setting himself up with an excellent chance to make it 3-0. Having picked up the ball just past the halfway line he skipped his way past three defenders before twisting to get his shot away, only to see it drag wide of the post.
He was replaced by Marko Marin on 78 minutes after proving that he can be effective as the only Amigo.
Yossi Benayoun returned to Chelsea in January from a loan spell at West Ham which saw him sidelined through injury for the vast majority of the time. He put in a good cross which was blocked but the left was dominated by Ryan Bertrand on the overlap.
Benayoun created the first goal when his attempted volley was blocked. The rebound fell kindly back to him and he played a diagonal ball back to Ramires to shoot and score. He was substituted almost immediately, with Eden Hazard replacing him for the final 30 minutes.
Torres was selected ahead of Demba Ba and got involved in a lot of build-up play. An attempted shot-cum-cross was easily dealt with by the Boro defence, and when he got his best chance of the half after 20 minutes, he opted for a tame shot which Jason Steele was able to easily deal with.
Despite this, he looks sharper than in recent weeks, in the same way that a butter knife looks sharper than a spoon. Ramires' goal deflected off of his shoulder, and he saw another shot blocked by Stephen McManus.
His frustration was evident as he looked toward the heavens and appeared to ask "why, why, why?" Unfortunately, nobody but Torres has the answer to solving his problems.
Eden Hazard joined the action after 60 minutes when Chelsea were already a goal to the good. He assisted in the second goal and had another two shots skim just wide of the post.
Hazard's influence on the game seems to be greater when he comes off the bench, and this game showed that Rafa Benitez could easily rotate him and Oscar as impact substitutes.