An early Richarlison strike and Gylfi Sigurdsson's second-half penalty secured the 2-0 win against the struggling Reds.
The result puts Everton level on points with Liverpool but also gives them a first win at their local rivals home ground since 1999.
After delivering something a generation of Toffees fans hadn't experienced, the manager's message was clear and hilarious in equal measure.
"Celebrate tonight with a good glass of wine and passion for Everton," Ancelotti told Everton fans in an interview with talkSPORT.
While Ancelotti was relatively restrained in celebrating the win, his players and assistant Duncan Ferguson most certainly were not!
Former player Ferguson embraced a number of the delighted Everton players as the final whistle blew.
The celebrations didn't stop there, though. There were jubilant scenes in the away dressing room which fans were given a sneak peek into thanks to Niels Nkounkou's Snapchat story.
See the video of Everton's celebrations over bitter rivals Liverpool above.
Carlo Ancelotti told Everton fans to enjoy 'a good glass of wine' following their momentous win over Liverpool at Anfield.