Antonio Conte’s side Chelsea moved to within one vicyory of the Premier League title and confirmed Middlesbrough's relegation with a consummate performance and emphatic win at Stamford Bridge.
The Blue side can become champions with win versus West Bromwich Albion at The Hawthorns on Friday night while Boro must contemplate a future back in the Championship after they were swept aside on Monday.
Chelsea had already created a succession of chances before striker Diego Costa turned in man of the match midfielder Cesc Fabregas' pass after 23 minutes.
And the contest was effectively over when defender Marcos Alonso netted at the far post via the legs of Middlesbrough goal keeper Brad Guzan 11 minutes before the break.
The Spain International created Chelsea's third which Serbian playmaker Nemanja Matic converted as the hosts laid siege to Middlesbrough’s goal, with the final whistle bringing contrasting emotions.
Chelsea manager Antonio Conte: "We must be pleased. It was a great performance, my players showed commitment and work-rate for three important points.
"At this stage it was important to win and exploit Tottenham's defeat. Now, another step to the title. We have to rest well and prepare for West Brom."
Middlesbrough boss Steve Agnew: "I am absolutely gutted and bitterly disappointed with the result and we have now lost our Premier League status which we took great pride in.
"I have just left a very silent dressing room.
"We haven't had enough wins and that's the key to the whole thing. Scoring goals wins football matches and we haven't done that enough this season.
"I have to say the fans all season have been outstanding - home and away has been top class and the least they deserve is Premier League football."