Goals from Diego Costa, Marcos Alonso and Nemanja Matic saw Chelsea re-establish a seven-point lead over Tottenham and relegated Boro. Antonio Conte's men can win the title before Spurs next play with victory at The Hawthorns on Friday night.
"This step was big, a big step for us. A big win," Conte said.
"Now we need to do another step. We have the possibility to do this on Friday against West Brom but for sure it won't be easy, because West Brom is a really good team, a physical team and we must pay great attention.
"Now we have three chances to exploit, to become champions.
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For sure, now we are very close."
Costa scored his 20th league goal of the season, converting a pass from the excellent Cesc Fabregas, and Alonso netted from a similar position before half-time before Nemanja Matic's second-half goal.
"It wasn't easy, but we did this. I must be pleased for the performance, for the commitment, for the desire, for the will of my players.
"It's great to score three goals, to create many chances and also for another clean sheet."
Conte believes Chelsea overcame their greatest challenge when defeat at Jose Mourinho's Manchester United last month cut their lead to four points over Tottenham, who the Blues then beat in the FA Cup semi-final.
Chelsea next defeated Southampton before a win at Everton and Monday night's success against Boro.
Conte said: "Our worst moment was after the United defeat, because Tottenham won the game and to see your opponent only four points (behind) was very bad.
"Then we had to play against them in the semi-final of the FA Cup.
"At that moment we had a lot of pressure, but in that moment my players showed me great commitment, great focus, desire to overcome this moment and to try to win the league.
"Now there is the pressure, but now it's a good pressure, a pressure that this pressure must bring in our heart excitement.
"The target is very close and we must have enthusiasm, will, desire to take this target. My players deserve to win the league."
Chelsea won the 2014-15 title under Mourinho but imploded and finished 10th last term as Leicester won the title.
Now Conte is on course for a double, with the Blues facing Arsenal in the FA Cup final on May 27.
Conte added: "Last season was very bad and this season, don't forget we started with a lot of problems.
"Now we were very good to find the right way and have a fantastic season. We need another step and then to celebrate."