Diego Costa slid in the opener, a Rolando Aarons error let in Pedro to run clear and fire home, and Costa set up Willian to make it 3-0.
Pedro and Bertrand Traore added further goals in the second half, before Andros Townsend's late consolation.
The only thing to spoil Chelsea's night was an injury to captain John Terry.
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The centre-half limped off with a hamstring injury before half-time and is a doubt for Tuesday's trip to play Paris St-Germain in the first leg of their last-16 Champions League tie.
Chelsea's interim manager Guus Hiddink remains unbeaten in 12 games in all competitions, and his side are now unbeaten in their past 10 Premier League games.
Newcastle have only scored seven goals on their travels this season, the worst record in the top four divisions in England, but it was their defence that let them down at Stamford Bridge.
Magpies boss Steve McClaren said in his pre-match TV interview that the first 20 minutes would be crucial to the outcome of the match. He was right, but not in the way he would have wanted.
By then, his side had suffered a complete collapse at the back which was summed up by Chelsea's second goal.
That came from a Newcastle free-kick near the home side's corner flag that was cleared to the halfway line before Aarons' horrendous cross-field pass allowed Pedro to gallop clear.
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McClaren's side never looked capable of a second-half comeback as they slipped to a fifth successive away defeat.
After the break, Cesc Fabregas set up Pedro for his second and Bertrand Traore turned in Cesar Azpilicueta's cross.
Andros Townsend's trademark run and finish for his first goal since his £12m move from Tottenham reduced the damage at the end.
But Newcastle's goal-difference still took a battering and at -22 it is now the worst in the top flight.
Chelsea's own defensive problems were of a very different sort.
With Kurt Zouma out for the season, the last thing Hiddink needed before a busy fortnight was to see Terry limp off.
Terry appeared to fall awkwardly after a clash with Magpies striker Aleksandar Mitrovic and will have a scan to assess the severity of his hamstring injury.
Gary Cahill only returned to the starting line-up on Saturday because of Zouma's serious knee injury, but could end up being a key figure at the back for his side in the next few weeks.
He was playing with a broken nose, but Chelsea's man in the mask did not miss his mark.
Along with the impressive Willian, Costa scored one goal and made another but he edged the individual accolade because of his delightful finish to give his side an early lead.
Chelsea manager Guus Hiddink: "We can be pleased with the performance of the guys. We tried to surprise them in the beginning. Happily it worked out.
"It's important for the way we played, not just in attack. The players also have to do defensive work and that is where we are aiming and then the quality comes out."
Newcastle boss Steve McClaren: "We got exposed on quite a few occasions in terms of defensive frailties. Rolando Aarons had to play at left-back and it was Steven Taylor's second game in six months.
"We caused our own problems. We knew Chelsea would come out quick. They wanted to win that game by half-time with the week they have ahead of them.
"You get one or two of these games a season. I've told the players don't let that derail us. It was damage limitation by half-time.
"I just wanted to make sure we scored a goal and stayed in the game."
Newcastle are out of the FA Cup and their Premier League game with Manchester City on 28 February has been postponed because City are in the Capital One Cup final.
So the Magpies do not have a game for 18 days until they travel to Stoke on 2 March, and are heading for a training camp in Spain.
In that time, Chelsea play four matches, starting with Tuesday's trip to Paris.
Match ends, Chelsea 5, Newcastle United 1.
Second Half ends, Chelsea 5, Newcastle United 1.
Delay over. They are ready to continue.
Delay in match Daryl Janmaat (Newcastle United) because of an injury.
Corner,  Chelsea. Conceded by Steven Taylor.
Goal!  Chelsea 5, Newcastle United 1. Andros Townsend (Newcastle United) left footed shot from outside the box to the bottom right corner. Assisted by Jack Colback.
Foul by Gary Cahill (Chelsea).
Seydou Doumbia (Newcastle United) wins a free kick in the attacking half.
Goal!  Chelsea 5, Newcastle United 0. Bertrand Traore (Chelsea) left footed shot from the centre of the box to the bottom right corner. Assisted by César Azpilicueta with a cross.
Substitution, Chelsea. Ruben Loftus-Cheek replaces Willian.
Attempt missed. Baba Rahman (Chelsea) right footed shot from outside the box misses to the right. Assisted by Cesc Fàbregas.
Attempt blocked. Cesc Fàbregas (Chelsea) right footed shot from outside the box is blocked. Assisted by César Azpilicueta.
Attempt blocked. Bertrand Traore (Chelsea) left footed shot from outside the box is blocked.
Corner,  Newcastle United. Conceded by Branislav Ivanovic.
Substitution, Newcastle United. Seydou Doumbia replaces Aleksandar Mitrovic.
Foul by Gary Cahill (Chelsea).
Rolando Aarons (Newcastle United) wins a free kick in the defensive half.
Willian (Chelsea) wins a free kick on the right wing.
Foul by Andros Townsend (Newcastle United).
Corner,  Chelsea. Conceded by Rolando Aarons.
Substitution, Newcastle United. Jamaal Lascelles replaces Cheick Tioté.
Corner,  Chelsea. Conceded by Jack Colback.
Foul by Jack Colback (Newcastle United).
Pedro (Chelsea) wins a free kick in the attacking half.
Foul by Cheick Tioté (Newcastle United).
Bertrand Traore (Chelsea) wins a free kick in the attacking half.
Jonjo Shelvey (Newcastle United) is shown the yellow card for a bad foul.
Foul by Jonjo Shelvey (Newcastle United).
Cesc Fàbregas (Chelsea) wins a free kick on the left wing.
Substitution, Chelsea. Bertrand Traore replaces Diego Costa.
Goal!  Chelsea 4, Newcastle United 0. Pedro (Chelsea) right footed shot from the centre of the box to the bottom right corner. Assisted by Cesc Fàbregas with a through ball.
Attempt missed. Aleksandar Mitrovic (Newcastle United) right footed shot from the right side of the box is close, but misses to the left.
Attempt blocked. Jonjo Shelvey (Newcastle United) right footed shot from outside the box is blocked. Assisted by Jack Colback.
Offside, Chelsea. César Azpilicueta tries a through ball, but Diego Costa is caught offside.
Corner,  Chelsea. Conceded by Rolando Aarons.
Foul by Rolando Aarons (Newcastle United).
Diego Costa (Chelsea) wins a free kick on the right wing.
Corner,  Newcastle United. Conceded by César Azpilicueta.
Attempt blocked. Jonjo Shelvey (Newcastle United) right footed shot from the centre of the box is blocked.
Attempt blocked. Aleksandar Mitrovic (Newcastle United) right footed shot from the centre of the box is blocked. Assisted by Andros Townsend with a cross.
Newcastle dropped into the relegation zone on goal difference after three goals in the first 17 minutes set Chelsea on their way to an easy win.