Chelsea advanced to the fifth round of the FA Cup after a brace from Belgian striker Michy Batshuayi and sublime freekick from Marcus Alonso against Newcastle at Stamford Bridge.
Chelsea took the lead in the 31st minute after a sublime pass from the Pedro to Hazard who unselfishly laid it down for Batshuayi, who finished cool, calmed and collected.
Batshuayi then doubled his side's lead just 13 minutes later to put them 2-0 up before half time and at 72 minutes Alonso added a third with a brilliant freekick.
Chelsea came into this fourth round tie on the back of a defeat to Arsenal on Wednesday night in the semi-final of the Carabao Cup at the Emirates and needed a win to overcome that loss. Chelsea, last year's runners-up in the FA Cup, were looking to continue their progress in this competition and make amends for last year's final.
Newcastle, however, making five changes for this tie, had one eye or maybe even both on their crucial upcoming Premier League game against Burnley on Wednesday night. They currently sit one point above the bottom three and their primary focus is on staying up not progressing to the fifth round.
However, it was Newcastle that started the better side using high press and going forward, whilst Chelsea began sloppy in possession in the middle, with Danny Drinkwater loosing possession early on.
Batshuayi's first touch of the game came in the 23rd minute, allowing the visitors to enjoy their first shot of the game just two minutes later. Willy Caballero was on hand for Chelsea and saved former Liverpool player Jonjo Shelvey's low shot by his feet.
But the architect of Chelsea's breakthrough was Pedro, who played a stunningly sweet pass to Hazard - the builder, who unselfishly laid the ball across goal to Batshuayi with a simple tap to take his side into the lead at 31 minutes.
But Newcastle continued to press and almost three minutes later, Newcastle found space with Dwight Gayle out-muscling Rudiger, but his left-foot effort was saved by Cabellero once again.
Chelsea didn't dare take their foot off the gas, with another goal only 13 minutes later. It was the trio once again of Pedro, Hazard and the finisher Batshuayi. Hazard, on the counter-attack, released Batshuayi once again who grabbed a huge slice of luck as his shot hit the shin pads of defender Jamaal Lascelles and past goalkeeper Karl Darlow.
The second goal of the game was Batshuayi's tenth goal of the season, with five goals in the FA Cup in eight matches.
The second half started as the first half ended, with Chelsea enjoying possession and they were nearly gifted a third as Lascelles lost possession and Pedro shot just over the bar.
After Pedro's moment of brilliance in the first half for the first goal, the third goal was down to Marcus Alonso. Chelsea, who seemed to not be reeling over their defeat against Arsenal, showed why they made the final last year.
Davide Zappacosta was brought down on the edge of the box and earned his team a free-kick. And up stepped Alonso. He was never going to miss that. Beautifully bent over the wall and beyond a despairing dive by Darlow, the ball smashed into the back of the net. Essentially, game over.
It wouldn't be an FA Cup tie without the introduction of some youngsters. Antonio Conte introduced Ethan Ampadu and Callum Hudson-Odoi late on.
Chelsea now look to their midweek fixture against Bournemouth in the Premier league after cruising to the fifth round.