The Blues beat Hull 2-0 at Stamford Bridge on Sunday and lead the Premier League by eight points after four of their five title rivals dropped points over the weekend.
Costa celebrated his 52nd Chelsea goal on his 100th appearance by gesturing about all the noise which has surrounded him since missing the win at Leicester, officially due to a back injury.
A reported bust-up with Antonio Conte and his staff, as well as speculation over a move to the Chinese Super League, had little impact on Costa, whose 15th goal of the season was followed by a Gary Cahill header.
Conte, who was too busy celebrating himself to see Costa's gesture, said: "It's important Diego played a good game.
"I hope with this game to finish the speculation about him, about Chelsea, about me and him
We showed we are a team with great unity."
The five-year deal Costa signed on his arrival from Atletico Madrid runs until 2019.
Conte reiterated Costa was happy and under contract
Asked about the prospect of a new deal, Conte said it would be a club decision before saying "why not?" when it was put to him that a new contract for the striker would be a mark of his commitment.
"I think his (current) contract put the end to all the speculation," the Italian said.
"He's very happy to stay with us
He's very happy to stay with Chelsea.
"I don't see any problem with Diego with this contract."
Rivals Liverpool, Manchester City, Tottenham and Manchester United all dropped points on Saturday and Arsenal narrowly avoided doing so on Sunday, giving Conte plenty of reasons to smile broadly.
"Today we had the pressure to win and to exploit this weekend," Conte added.
"For sure this game wasn't our best game, but I think it's normal
We are in the second part of the season and the points now are heavy for us.
"A lot of opponents dropped points this weekend and for sure I'm pleased, because it's not easy to play the last game of the weekend and to know the results of the other teams.
"To win this type of game and to exploit the situation that the other teams dropped points is very important
I'm sure about this."
Conte was adamant the title is not already Chelsea's to lose
He said his teams have conceded and overturned seven-point deficits with four games to go in the past.
The former Juventus boss added: "Now we have (a lead of) eight points and there are 16 games to play.
"I think me, my players, we have good experience to understand that this league it'll be very tough until the end.
"To stay now in that position is fantastic for us
At the start of the season not one person thought this."
Hull's ninth straight away loss was marred by a head injury to Ryan Mason, who was carried off on a stretcher as oxygen was administered
Curtis Davies also went off injured.
The visitors wanted a penalty early in the second half and felt aggrieved when Marcos Alonso's challenge on Abel Hernandez went unpunished.
Hull boss Marco Silva declined to comment on the decision.
"I'm here to talk about the game," he said.
"I don't know
I'm sure you (the media) know better than me.
"I don't stay happy with the result
We tried to come to compete and to take points
It's not a bad performance for us.
"We have some problems in the first half
We had good defensive organisation."
Silva was without the injured Robert Snodgrass amid speculation over the Scotland midfielder's future.
Asked if Snodgrass would be leaving Hull this month, Silva said: "I don't know
I hope no, because I want the player in the squad.
"He's a good player, an important player for us
Important players for us I don't want to leave."
Silva instead wants to enhance his squad.
He added: "I'm sure we will improve more in the next weeks
We will improve our squad also.
"We need to put more players and more quality here to help our squad
I'm sure we will improve."
Source : PA