Costa, 28, underlined his importance to Chelsea with his 15th strike of a prolific campaign deep into first-half stoppage time, while skipper Gary Cahill secured the Blues’ 15th win in 16 top-flight matches inside the final 10 minutes.
It was Costa’s first appearance for the Stamford Bridge club since being omitted from their squad to face Leicester last week after reports of a bust-up with a fitness coach and a jaw-dropping financial offer from the Chinese Super League.
“It was important for Diego to play a good game,” said Conte. “I hope this game finishes the speculation about him, about Chelsea, about me and him, because I think that we showed that we are a team with a great unity.
“Diego has two years left on his contract with Chelsea. His contract puts an end to all the speculation and, I repeat, he is very happy to stay with us and very happy to play with Chelsea. The present is more important than the future.”
While Conte refused to accept that the title was now Chelsea’s to lose, the Italian insisted that it was crucial to take advantage of their rival's travails. Arsenal were the only other team in the top six to win at the weekend.
“To win this type of game and to exploit the situation that the other teams dropped points is very important, I am sure about this,” added Conte. “To be in this position now is fantastic.”
Costa’s reintegration into the Chelsea fold was almost complete within 10 seconds. A headed clearance from Hull centre-half Curtis Davies following David Luiz’s punt forward was seized upon, controlled and volleyed inches wide by the seemingly eager to impress frontman.
Although Hull were proving a tough nut to crack, the deadlock was broken in the seventh minute of first-half stoppage time, allotted following a head injury to former Tottenham midfielder Ryan Mason which required lengthy treatment.
Chelsea’s goalscorer, inevitably, was Costa as he side-footed first-time beyond Hull goalkeeper Eldin Jakupovic after Victor Moses was afforded time to produce a low, skimming cross by visiting wing-back Andrew Robertson.
The Blues escaped Hull’s claims for a penalty after Marcos Alonso clumsily felled Abel Hernandez moments into the second period, while Thibaut Courtois was forced to repel an effort from Mason’s replacement David Meyler.
But despite Chelsea being far from their fluent best, the clash was settled in the 81st minute as a floated, inswinging free-kick from substitute Cesc Fabregas was glanced past Jakupovic by Cahill.