Newcastle, threatened with relegation from the Premier League, had seen Ciaran Clark score a surprise equaliser before half-time after an early goal from Pedro put Chelsea ahead at Stamford Bridge.
But with the Magpies making life tough for their hosts, Willian’s brilliant curling shot in the 57th minute secured all three points for the Blues.
It was just his fifth goal of the season and first in the league since October but Willian told BT Sport: “I think it’s always difficult in the Premier League.
“We have to be more clinical… I scored a good goal. I found the space and put the ball exactly where I wanted.”
Willian has been repeatedly linked with a move away from Chelsea but he was adamant he wanted to stay at the west London club.
“My future is here at Chelsea, I don’t know what you’re talking about,” he said.
Chelsea manager Maurizio Sarri was equally keen for Willian to remain a member of his squad, especially as he is deploying Eden Hazard as a striker.
“You know very well that Willian for us is a very important player,” Sarri told reporters. “In my opinion, Willian has to stay with us.
“With Eden playing as a striker we need wingers. In this moment he is a fundamental player.”
Victory saw fourth-placed Chelsea open up a six-point lead over London rivals Arsenal in the race for a place in next season’s Champions League.
But Sarri was unhappy with the way the Blues struggled to see off a Newcastle side stuck in the relegation zone.
“I am very happy with the result but the performance was not so good, especially between 1-0 and 1-1,” he said.
Newcastle manager Rafael Benitez was proud of the way his players had pushed Chelsea hard but accepted they had been undone by a sublime goal.
“We conceded a goal we could avoid but after that we were fighting for every ball; these players care you could see that,” Benitez told the BBC.
“We scored and then controlled the last few minutes of the first half so it’s a pity but a piece of quality made the difference.
“You could see a lot of positives with the performance but no points.”
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