The London side showed plenty of attacking flair but it was not a vintage performance.
The Premier League leaders were missing several injured stars and never got out of second gear against a disappointing home side.
Middlesbrough manager Gareth Southgate must have been bitterly disappointed with the performance of his team.
Boro lined up with five in midfield and Mido as the lone striker, with local hero Stewart Downing making his 200th appearance at the age of 23.
Chelsea welcomed the return after injury of John Terry and there was an encouraging chant of "there's only one England captain" from the visiting fans.
The Blues soon got into their stride and after only 14 minutes Salomon Kalou scored an easy goal after a deflection.
Soon after, home midfielder Gary O'Neil was booked for a foul though the decision was harsh.
Middlesbrough struggled to get into the game and the only surprise of the first half was that Chelsea had only one goal to show for their efforts.
Southgate must have hoped for second-half improvement but Middlesbrough's hopes were dashed with a superb strike by Juliano Belletti from 30 yards.
The power and accuracy of his shot left goalkeeper Ross Turnbull completely helpless and it will certainly be a candidate for goal of the month.
Kalou added a third almost immediately with a shot that struck centre-half David Wheater on its way into the net.
The rout continued as Kalou provided a perfect cross for Frank Lampard to score with a header.
When a Nicolas Anelka shot was fumbled onto a post by Turnbull, Florent Malouda pounced to score an easy goal from close range.
Chelsea were without several stars but they obviously have the strength in depth to mount a serious title challenge this season.
There were empty seats in the stands long before the final whistle as Middlesbrough fans made their way to the exits.
This was one of the Boro's poorest performances in recent years at Riverside Stadium and Southgate faces a tough challenge to lift his players.