The Blues took control with three goals inside the opening 17 minutes.
Diego Costa, playing in a face mask after suffering a broken nose in training, set the hosts on their way after five minutes when netting from close range.
Newcastle were opened up again only four minutes later when Pedro latched onto a stray pass to race clear and slot past Rob Elliott before Willian effectively ended the match as a contest.
Spanish forward Pedro slotted number four just before the hour and Chelsea substitute Bertrand Traore made it 5-0 with eight minutes left.
Newcastle winger Andros Townsend, a £12million signing in January, broke the hosts' clean sheet in the final minute.
Struggling Sunderland boosted their Barclays Premier League survival hopes with a 2-1 victory over lacklustre Manchester United at the Stadium of Light.
The Black Cats went ahead inside three minutes of Saturday's lunchtime match with a curling free-kick from Wahbi Khazri.
United levelled six minutes before half-time through Anthony Martial.
However, Louis van Gaal's side failed to build any momentum and were beaten after Lamine Kone's header deflected in off goalkeeper David de Gea with eight minutes to go.
United are now just a point ahead of Southampton, who claimed 1-0 win at Swansea.
A solitary header from Shane Long on 69 minutes was enough to extend The Saints' unbeaten league run to six matches, and without conceding a goal.
Struggling Norwich blew a 2-0 lead as West Ham fought back to draw 2-2 at Carrow Road.
Barclays Prem
1 Leicester 53
2 Tottenham 48
3 Arsenal 48
4 Man City 47
5 Man Utd 41
6 So'ton 40
7 West Ham 40
8 Watford 36
9 Stoke 36
10 Everton 35
11 Liverpool 35
12 Chelsea 33
13 C Palace 32
14 W Brom 32
15 B'mouth 28
16 Swansea 27
17 Norwich 24
18 Newcastle 24
19 S'land 23
20 A Villa 16
The Canaries, who had lost five successive games to plummet into the bottom three, went ahead through a fine curling effort from Robbie Brady on 54 minutes before Wes Hoolahan doubled their advantage from close range on 65 minutes.
However, West Ham midfielder Dimitri Payet marked his new contract extension with a neat finish from a tight angle on 74 minutes before Mark Noble silenced the home supporters when crashing in a equaliser just two minutes later.
Stoke won their first Premier League match since January 13 with a 3-1 victory at Bournemouth.
The away side took the lead on nine minutes when £18.3million signing Giannelli Imbula cracked in a 25-yard volley.
Stoke scored again early in the second half through a close-range finish from Dutch midfielder Ibrahim Afellay on 52 minutes.
Before Bournemouth could regroup, they were 3-0 down when Stoke substitute Joselu, having only just come on, headed in on 55 minutes.
The hosts this time quickly hit back through half-time substitute Matt Ritchie in the 57th minute, but Stoke went on to close out a comfortable victory.
Troy Deeney scored twice as Watford secured a 2-1 victory at Crystal Palace, who remain without a Premier League win since December 19.
The visitors went ahead on 16 minutes when Deeney converted a penalty.
Palace levelled in first-half stoppage time through a looping header from Emmanuel Adebayor, the much-travelled Togo frontman's first Premier League goal since October 2014.
However, with just eight minutes left, it was the Hornets who secured all three points when Deeney swept home.
Palace midfielder Yohan Cabaye hit the post in stoppage time, before defender Pape Souare was shown a straight red card for a two-footed challenge on Valon Behrami.
West Brom returned to winning ways with a battling 1-0 victory at Everton.
The Baggies, who beat Peterborough on penalties in the FA Cup fourth round in midweek, were in front on 14 minutes when Salomon Rondon bundled the ball over the line.
Everton pressed for an equaliser and hit the post through Ross Barkley, but could not find a way back into the match as West Brom won in the league for the first time since January 2.