The Blues needed to come from behind after Dwight Gayle had given the out-of-form Magpies a shock lead in West London, but Eden Hazard's brace either side of an Alvaro Morata header sealed a sixth win in the space of seven Premier League games for Chelsea.
The result sees the hosts temporarily close the gap on leaders Manchester City to eight points, whereas Newcastle have now taken only one point from the last 18 on offer in the Premier League.
The champions welcomed Hazard and Cesar Azpilicueta back into their starting lineup after they were rested in midweek, but Chelsea made a sloppy start to the match as Newcastle settled quickly.
Both sides had half-chances in the opening exchanges as Mikel Merino's tame effort was collected by Thibaut Courtois before Morata lashed a snapshot off target from a tight angle, but it was the Magpies who took a shock lead after 12 minutes.
Newcastle's high press yielded rewards as Marcos Alonso sold Courtois short with a back-pass, forcing the keeper to come off his line and get to the ball ahead of Jacob Murphy. However, his touch only took the ball to the feet of Gayle, who was left with a simple finish into the empty net.
The goal only seemed to spark Chelsea into life, though, and it took a stunning save from Karl Darlow to keep his side ahead five minutes later after Hazard had collected a brilliant pass from Cesc Fabregas inside the penalty area.
Morata was then denied a penalty despite being clipped by Darlow inside the area, and Chelsea continued to knock on the door when Andreas Christensen hit the outside of the post with a header moments later.
The equaliser seemed inevitable, and sure enough it arrived just one minute after Chelsea had struck the woodwork when Florian Lejeune's clearance only fell as far as Hazard, who fired a volley into the ground and bouncing past a helpless Darlow.
There was no let-up from the hosts, though, and they had completed the comeback shortly after the half-hour mark when Morata converted a powerful Victor Moses cross from close range after both Lejeune and Chancel Mbemba had failed to intercept the ball.
Danny Drinkwater then sent a long-range strike swerving wide of the target as Newcastle avoided any further damage before the break, but Chelsea came out quickly at the start of the second too and it took an important interception from Mbemba to deny Morata an early goal after the restart.
Chelsea continued to dominate, though, and Hazard looked the most likely to give his side a cushion during another dazzling display from the Belgian.
The winger saw one powerful effort deflected narrowly wide before showing remarkable close control and balance in the area, only to be thwarted by Darlow at the end of his run.
Moses then glanced a header straight at the Newcastle keeper from Azpilicueta's cross, but the spotlight was soon back on Hazard as he forced another stop from Darlow before narrowly missing the chance to get on the end of a one-two with Drinkwater.
The Belgian's second goal eventually arrived from the penalty spot with a little over 15 minutes remaining, sending Darlow the wrong way with a cheeky Panenka dink after Matt Ritchie had brought Moses to ground inside the area.
Hazard could have capped his impressive individual performance with a hat-trick just two minutes later having been slid through by Morata, but Darlow stayed on his feet this time to deny another chipped effort from the winger.
In the end, Antonio Conte ended any further hat-trick chances by withdrawing Hazard with 12 minutes remaining, but that didn't stop Chelsea from pushing for a fourth and Alonso became the latest to test Darlow with a powerful strike from a tight angle.
Newcastle did threaten a late consolation when Ciaran Clark nodded over from a corner in the final minute, but the match was over as a contest by that stage as Rafael Benitez suffered defeat on his first return to Stamford Bridge since his time as Chelsea boss came to an end.
The Magpies have now lost five of their last six league games and have only won one of their last 19 away games in the top flight, whereas Chelsea record a fifth consecutive win at Stamford Bridge across all competitions.
The champions are now level with United ahead of the Red Devils' trip to face fellow top-four rivals Arsenal this afternoon, while leaders Manchester City are not in action until Sunday.
Chelsea (3-5-1-1): Courtois; Azpilicueta, Christensen (Cahill, 80'), Rudiger; Moses, Kante, Drinkwater, Fabregas (Bakayoko, 78'), Alonso; Hazard (Willian, 78'), Morata
Newcastle United (3-4-3): Darlow; Manquillo, Clark, Lejeune, Mbemba; Ritchie, Merino (Yedlin, 85'), Diame (Shelvey, 75'), Murphy, Perez (Hayden, 62'); Gayle