The England centre-half equalised in the 14th minute to help Chelsea get back on level terms five minutes after Liverpool midfielder Emre Can’s opener in Saturday’s early kick-off.
Spain international Diego Costa scored what proved to be the winner with 23 minutes remaining, cementing Chelsea’s spot at the top of the Premier League.
And Cahill, who has four goals in 72 top-flight appearances for the Blues, took to Twitter to thank the travelling fans for their support.
Great result today, incredible support from #CFC fans as always
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news