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.
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 after the break.
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.
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.