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.
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