Nicolas Jackson's instinctive sixth-minute opener for the Blues was cancelled out on the stroke of half time by a superb strike from Magpies frontman Alexander Isak.
However, Cole Palmer - who assisted Jackson's opener - restored Chelsea's advantage by netting his 11th Premier League goal of the season midway through the second half, before substitute Mykhaylo Mudryk added a third in the final 15 minutes.
A 90th-minute thunderbolt from Jacob Murphy gave Newcastle hope of a late comeback, but Chelsea held on to claim three precious points as well as their fifth win in six top-flight games at Stamford Bridge.
Mauricio Pochettino's side remain 11th in the Premier League table despite victory, but they have moved to within one point of Eddie Howe's men in 10th place, while they are now only four points behind West Ham United in seventh spot.
Seeking to bounce back from successive league draws with Manchester City and Brentford, Chelsea did not take long to put their stamp on proceedings against Newcastle and opened the scoring courtesy of a slice of misfortune from the Magpies and a moment of intuition inside the penalty area from goalscorer Jackson.
Following a bursting run and cross from the right by Malo Gusto, Newcastle defender Sven Botman made a mess of his clearance which rolled into the path of Palmer, whose strike from distance, which may have been going wide, was cleverly flicked by Jackson, with his back to goal, into the bottom corner.
Newcastle struggled to get going and their attempts to restore parity were made all the more difficult when star winger Anthony Gordon was withdrawn in the 35th minute with an apparent knee injury, following a coming together with Marc Cucurella - a big blow for the Englishman with Gareth Southgate watching on from the stands.
Murphy came on as Gordon's replacement and was immediately involved, teeing up Miguel Almiron at the back post before the Paraguayan delivered an inviting cross into the danger zone for Joe Willock, but Cucurella got back well to distract the Magpies midfielder as he poked the ball over the crossbar.
Chelsea initially looked comfortable as they approached half time, but a poor two to three minute period during which both teams gave the ball away on numerous occasions resulted in Newcastle winning back possession and netting a superb leveller in the 43rd minute.
After receiving a smart flicked through-ball from Bruno Guimaraes, Isak took a couple of touches to set himself on the edge of the area, allowed space after Axel Disasi surprisingly backed off, before placing a beautifully-struck side-footed shot beyond Djordje Petrovic into the bottom corner.
Jackson thought he has put the Blues back in front just a few minute later, but the Senegalese striker was caught offside before drilling a shot beyond Martin Dubravka, not long after the Slovakian shot-stopper stood firm to keep out a powerful strike from Raheem Sterling.
In stark contrast to the first 45, Newcastle made a bright start to the second half, with a fierce strike from Almiron stinging the gloves of Petrovic, who turned the ball over for a corner. Bruno Guimaraes then whipped a dangerous cross into the corridor of uncertainty following a short corner, but no Magpies attackers were busting a gut to meet the delivery that curled out for a goal kick.
Chelsea responded well with a perky passage of play in the final third, and they got themselves back in front on the 57-minute mark when Palmer found a pocket of space in between the lines before unleashed a devastating left-footed shot from around 20 yards out into the bottom-left corner.
Palmer has now scored in five consecutive home starts for Chelsea and has also become the first player in the Premier League to both score and assist in a single match on five occasions this season.
Pochettino's men came close to adding a third just a few minutes later when Sterling races through on goal and used his composure to work the ball around Dubravka, before taking a delayed shot that was blocked on the line by Dan Burn.
Newcastle's injury woes showed no sign of letting up as Burn was forced off in the final 25 minutes after landing awkwardly to defend a deep set-piece from Chelsea, with Emil Krafth brought on as his replacement.
Mudryk was brought on by Chelsea not long after Krafth introduction for the visitors, and the Blues winger made his mark following a swift counter-attack in the 76th minute when he surged between two tackles before rounding Dubravka to tap home the hosts' third from a tight angle.
Out of nowhere, Magpies winger Murphy rolled Cucurella and smacked an audacious strike from a tight angle on the right side of the penalty box into the top corner, setting up a nervy finish for the hosts.
The Blues failed to win any of their last three Premier League games in which they led by a 1-0 scoreline, but they managed to see out the six minutes of stoppage time to claim all three points against the Magpies.
Chelsea and Newcastle will now shift their focus to the FA Cup quarter-finals, with Howe's side taking on holders Manchester City at the Etihad Stadium on Saturday, a day before Pochettino's men play host to Championship leaders Leicester City.