The Belgian's goals could not have been better timed with reports suggesting that Chelsea are close to signing a striker ahead of Wednesday's transfer deadline.
Batshuayi was one of four changes from the team knocked out of the League Cup in midweek and Antonio Conte's show of faith in his reserve striker was quickly rewarded when he got on the end of a slick move started by Pedro's probing pass to put Chelsea ahead on 31 minutes.
Although Batshuayi seldom gets game time in the Premier League, he remains the Italian's go-to man in the FA Cup, with no Chelsea player having scored more in the competition under Conte.
Another strike quickly followed although this time Batshuayi needed a huge slice of luck when, set free by Eden Hazard, his shot was deflected over the keeper by the diving Jamaal Lascelles just before the break.
The goal was Batshuayi's 10th of the season. Asked after the match about his future, the striker said: "I don't know, it's better you speak to Conte.
"When I have a chance I want to take it. I work every day and today I am very happy here."
Marcus Alonso added Chelsea's third just after the interval with a superb 72nd-minute freekick over the wall.
While Chelsea have been in the fifth round 18 times in the past 20 years, Newcastle last reached that stage in 2006.
Cardiff City host Manchester City in the day's other game later on Sunday.
(Reporting by Neil Robinson, editing by Pritha Sarkar and Clare Fallon)
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