Jamaal Lascelles gave the Magpies a 1-0 lead close to half time, before two goals in the final 10 minutes from Moussa Sissoko and Andros Townsend put the gloss on a morale-boosting victory for Rafael Benitez, who secured his first win as manager.
There was also two reasons to celebrate for goalkeeper Karl Darlow, who managed his first Premier League clean sheet in the victory over City.
It has been an eventful few weeks for third-choice stopper Darlow, who was thrust into the spotlight following a long-term injury to Rob Elliot - the man deputising for first-choice Tim Krul, and deputising well at that.
But the Republic of Ireland goalkeeper took to Twitter on Saturday evening to acknowledge Darlow's achievement, noting it should be the first top-flight clean sheet of many in the years to come for the 25-year-old.
Congrats @KarlDarlow on 1st prem clean sheet. One of many to come!!— Robert Elliot (@the_dilsh) April 16, 2016
Benitez's men stay 19th in the table, but closed to gap to 17th-placed Norwich City - who have played one game more - to just three points now.
Sunderland, in 18th, also helped their survival prospects by smashing Norwich 3-0 at Carrow Road earlier on the Saturday. The Black Cats, who also boast a game in hand, are one point behind the Canaries.