The Brazilian curled home what proved to be the Blues' winner at Stamford Bridge after 57 minutes, making it 2-1 against a stubborn Magpies side.
Pedro had opened the scoring for the hosts after just nine minutes, before Ciaran Clark levelled prior to the break to set nerves on edge at Stamford Bridge.
Certain reports have suggested that Willian is unsettled in west London and looking for a way out of the club he has represented since 2013.
Barcelona has been mooted as a possible destination, with Blaugrana flop Malcom rumoured to be part of a potential deal to take the player to Catalunya.
But Willian gave the topic short shrift after his match-winning turn at the weekend.
"My future is Chelsea, I don't know what you're talking about," he fired to BT Sport when quizzed on his transfer situation.
Fellow goalscorer Pedro also chimed in, stating to his team-mate "your future is here".
Chelsea manager Maurizio Sarri added his voice to those playing down the transfer rumours.
"Willian is very important for us. He is a great player. I think that he has to stay with us," the Italian stated.
Prior to Saturday's kick-off, Sarri had also moved to pour cold water on a possible Willian-Malcom swap.
"I think he can do better, because the potential is higher, but he's very important for us, so I think it's impossible to lose him in January," he explained.
"I didn't receive anything [about Willian] yesterday [Thursday]. You'll have to ask the club and ask about the market, because if you ask me about the market you put me in trouble, because I don't know."