Chelsea stopped the rot after successive Premier League defeats as they ground down Hull at the KCOM Stadium.
The hosts enjoyed the better of a cagey first half but went behind when Willian swept home a curling shot after good work from Diego Costa after the break.
Costa found the top corner with a similar strike to double the lead after Nemanja Matic's powerful run.
Hull never recovered and could have been further behind but for Pedro's poor finishing from six yards.
Changed formation, changed fortunes
Chelsea manager Antonio Conte promised "a solution" after his side went down with a whimper against Arsenal last weekend and he found his answer in a strategy he used at former club Juventus.
The Italian opted for a three-man defence during much of this trophy-filled time in Turin and deployed Gary Cahill, David Luiz and Cesar Azpilicueta at the back as he organised his Chelsea rearguard to match.
It did not initially appear to have stabilised a side who had conceded nine goals in their last four games in all competitions.
Luiz lost track of Dieumerci Mbokani as he apparently struggled with the extra space he and his team-mates had to cover and was fortunate that the Hull striker's control betrayed him.
But the defence, along with the team as a whole, improved markedly after half-time and never looked like blemishing only their second clean sheet of the season.
Moses delivers message
The chief beneficiary of Conte's reorganisation was Victor Moses.
The 25-year-old's last Premier League start for Chelsea was in a 2-1 win over Aston Villa in May 2013 when Ashley Cole, Frank Lampard and Juan Mata were among his team-mates.
Loan spells at Liverpool, Stoke and West Ham followed, but the Nigeria international should not have to wait as long for his next appearance.
Playing as a right-sided wing-back, he was industrious and inventive and might have earned a first-half penalty when his trickery lured Hull forward Adama Diomande into a rash challenge.
Willian and Costa's precise efforts decided the destination of the three points, but Moses will be most pleased with his day's work.
Reality catching up with Hull
Even the most ardent Hull fan will not have expected their season to continue in the way it started.
But equally they will be alarmed by how the Tigers' form has flat-lined after wins over champions Leicester and Swansea in their first two games. They have taken just one point from their last five games and are three points above the relegation zone.
Had Robert Snodgrass's early deflected effort not been brilliantly tipped over the top by Thibaut Courtois, it might well have been different.
But the hosts' defensive resilience wilted in the second half and the more they chased the game, they more vulnerable they looked.
The uncertainty over manager Mike Phelan's contract is an unwelcome distraction for a side who will need to be fully focused to turn their scant resources into survival.
Man of the match - Victor Moses
What they said
Hull caretaker manager Mike Phelan: "We were quite pleased we created a few issues for them in the first half, but we expect a team like Chelsea to ramp up the pressure a little bit.
"It has been difficult to get forward but we're not playing Mickey Mouse teams here. We have to be sensible with our approach and can't just be open against these teams.
"My situation has fluctuated from week to week but we're not far apart. We are talking and having lunches together, the owners and I. It's just a case of where it all stands.
"Now we have to get together and move forward. We have a few more games now where we can hopefully be competitive. I don't think there's any issues with the players who are here, they are trying to win football matches.
Chelsea boss Antonio Conte: "Every game is very tough in England and I am pleased with our performance because we scored two goal and got a clean sheet. I saw the right pressure and the right intensity from the players.
"After these two defeats it's not easy to work because two defeats for Chelsea are heavy defeats. But this was a good answer.
"I saw many of the players with great commitment, attitude and will to change the situation. I am pleased for them.
"We must follow this with work, work, work!"
The stats you need to know
- Chelsea kept their first clean sheet in eight away Premier League games, since a 4-0 win at Aston Villa in April.
- Since Diego Costa joined Chelsea, only Sergio Aguero (55) and Harry Kane (48) have scored more Premier League goals than the Spain international (38).
- In all competitions, Chelsea are unbeaten in their last 13 meetings with Hull, winning 11 and drawing two.
- Since Adama Diomande's strike against Leicester on the opening day, Hull have failed to score a first-half goal in each of their last six Premier League matches.
- N'Golo Kante made more passes (79), more successful passes (70) and had more touches (95) against Hull than he had in any of his previous 43 Premier League matches.
What's next?
Hull take the long trip to Bournemouth on Saturday, 15 October after the international break. Chelsea are at home to champions Leicester on the same day in the 12:30 BST kick-off.