The Blues stretch their winning run to six games as they go top of the Premier League in the twelfth match week of the season, as Costa inspires his team despite being half-fit
Chelsea had to battle past Middlesbrough who were tough and dogged, but were defeated after Costa reacted quickest in the 41st minute to win a second ball and slot past an in-form Victor Valdes.
The 28-year-old proved how important he is to Antonio Conte's side after being used over Michy Batshuayi despite missing his international games for Spain due to a thigh injury sustained against Everton.
Costa stretches remarkable scoring run
He appeared to be suffering few ill effects as he provided Chelsea with a complete performance that improved as the game wore on. Aside from his goal, his hold up play was an example for all strikers, at any level, including his cushioned header that Pedro slammed against the bar in the 62nd minute.
Costa drew fouls and got in behind as well as operating in a number 10 role at times, which all helped to take pressure off Chelsea who were increasingly sitting back in a tough second half.
Victor Moses was another who had the chance to kill off Boro at the Riverside Stadium, after Costa drove through the middle of the park and delivered a perfectly timed through ball, only for Moses to blaze over.
Costa has been devastating from set-pieces this season, but also away from home earning his side vital points against Watford, Swansea City, Southampton and, now, Middlesbrough.
He has continued his run as the Premier League's top goalscorer, adding a ruthless side to his already brilliant all-round game. 10 goals in 12 games, coupled with three assists mean that he has contributed to more goals than any other player in the Premier League.
Costa fires Blues to the summit
Meanwhile, the Blues put in a strong and solid away performance as a full team, with the likes of Eden Hazard playing a vital role in the win, and the midfielders and defenders holding firm in their individual and collective battles.
His interplay with the likes of Hazard and Pedro is fluid, as Costa is able to drop deep to allow Hazard to run behind if it looks like a counter attack would be a better weapon than their usual approach to dominate possession.
In fact, he hasn't been booked since Chelsea's last defeat away to Arsenal and his yellow card record has become as good as Thibaut Courtois's clean sheet record in recent weeks.
It is reductive to say Costa is the only reason with Chelsea now gaining the best defensive record in the Premier League after a sixth clean sheet in a row, but Costa may be the player that Conte would least like to see injured and as he is essential to everything Chelsea do.
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Forget Sergio Aguero, Zlatan Ibrahimovic or Harry Kane as Costa now sets the standard as the most decisive all-round centre forward in the Premier League, and could lead the charts for the rest of the season.
If Costa is fit, Chelsea will fancy their chances to beat anyone with each player bringing the best out of each other in the new 3-4-3 formation. A worry may come on the day that Chelsea have to play without Costa in the league, but they will hope that day never comes.