Costa's 10th goal of the season was enough to ease the Blues to a 1-0 victory at the Riverside Stadium - their sixth in succession in the league without conceding - and ahead of Liverpool and Manchester City.
The 28-year-old Spain international's temperament was questioned at times during his first two seasons at Stamford Bridge, but the penny now appears to have dropped and his manager could hardly be more delighted.
Conte said: "For me, it's important to have this type of question because in the past, you asked me about his behaviour, about his reaction, about his patience.
"Now I think he is one of the best strikers in the world and he has to continue in this way, showing his patience, but in the right way.
"He is very focused on the team, to help the team with the ball, without the ball and he is scoring a lot of goals
He has to continue so."
Costa's 41st-minute close-range strike ultimately separated the teams on a day when keeper Victor Valdes and the woodwork kept Boro in it until the death, although Aitor Karanka's men were unable to take advantage of a series of half-chances which came their way to grab a point.
Lone striker Alvaro Negredo forced the one meaningful save Thibaut Courtois had to make, but struggled to emulate Costa's influence at the other end of the pitch.
Asked how the frontman could contribute further, Karanka said: "Going in the way he is going, working as he is working, fighting as he is fighting against everybody, and knowing he is not playing for Chelsea or Manchester City, he is playing at Middlesbrough and he is not playing with the team-mates that he's had in the past or the team-mates Costa has at Chelsea."
The new leaders entertain Tottenham next Saturday already anticipating the busy Christmas programme, but prepared for what lies ahead.
Conte said: "We are ready, we are ready to play many games in few days because from the start of the season, we have worked a lot, not only on the tactical aspect, but the physical aspect and we continue to work because in this league, it's important to have in every game high intensity, to have strength and to run from the start until the end - and also to have good technique and good talent."
Source : PA