The France midfielder marked his home debut with a 68th-minute strike to level the game at 2-2 and then blasted home a brilliant winner to further boost Alan Pardew's survival mission.
Chelsea looked to be on their way to a first victory in four attempts in all competitions when, after Frank Lampard had cancelled out Jonas Gutierrez's first-half opener by scoring his 10th Barclays Premier League goal of the season for the 10th successive campaign, Juan Mata curled home a superb 61st-minute effort.
But a rejuvenated Newcastle refused to accept defeat and Sissoko snatched a dramatic win which was secured when Steven Taylor blocked Lampard's goal-bound effort deep into injury-time.
It was meant to be striker Demba Ba's day as he returned to St James' Park, where he had given sterling service in his 18 months in a black and white shirt.
But having arrived to a less than harmonious welcome, with some Newcastle fans accusing him of chasing the money by heading for Stamford Bridge last month, he departed prematurely with a bloodied nosed to more catcalls after just 42 minutes.
The Magpies followed him down the tunnel just a few minutes later with the advantage at the end of a thoroughly entertaining 45 minutes of football.
While Ba's departure from Tyneside might have come as a major blow to Pardew, the early signs are that the recruitment drive launched in response was astutely conducted.
The confidence gained in Tuesday night's 2-1 victory at Aston Villa with new boys Mathieu Debuchy, Sissoko and Yoan Gouffran in the team was in evidence as the home side set about their task with some relish.
Papiss Cisse, the man Pardew hopes will supply the goals which once came from Ba, saw a fifth-minute effort blocked by defender Gary Cahill, but then failed to test returning keeper Petr Cech adequately when played in by Sissoko after 20 minutes and then Yohan Cabaye 16 minutes later.
Cabaye and full-back Davide Santon both sent rasping volleys just off target in an end-to-end contest in which the Magpies gave as good as they got.
However, Chelsea might have gone in front twice, Lampard blasting high over from Ashley Cole's 15th-minute pull-back, and then Ba forcing a 32nd-minute save from Tim Krul before heading the rebound inches wide under pressure from Fabricio Coloccini, whose boot caused the damage which forced his exit.
The opening goal eventually arrived four minutes before the break and from an unusual source.
Newcastle's final ball had at times been ordinary, but Santon produced a telling cross to allow Gutierrez to glance a deft header across Cech and into the bottom corner to send the home fans into raptures.
They were equally pleased to see the back of Ba seconds later but, as the whistle sounded, there was a general acceptance that they would need to produce a much better second-half display than they did at Villa Park if they were to hold on to their advantage.
Chelsea returned in determined mood to pin the Magpies back into their own half, and as Pardew's men retreated, Cisse found himself isolated in attack despite the best efforts of Sissoko and Gouffran.
They were back on terms within 10 minutes in stunning style when Lampard controlled Cole's pass on his chest, took another touch and then lashed a dipping shot past the helpless Krul.
Things might have been worse for Newcastle on the hour when James Perch gifted the ball to Oscar and the visitors broke at pace for Mata to cross for Lampard, but he headed straight at Krul.
The Dutchman was not so fortunate seconds later, however, when Torres laid the ball back to Mata, who curled a superb left-foot shot over Krul and into the top corner.
John Terry only just managed to prevent Cisse from connecting with Santon's 65th-minute cross in front of goal, but Krul had to back-pedal hurriedly to keep out Branislav Ivanovic's speculative effort from his own half a minute later.
However, the home side dragged themselves back into it with 22 minutes remaining when, after Cech had parried Gouffran's effort, Sissoko steered the rebound home.
Cech had to be at his best to palm away Sissoko's searing drive after he had run away from Cole down the right, and the former Toulouse midfielder tore the Blues open once again seven minutes from time before cutting inside Cahill, only to toe-poke his effort straight at Cech.
But the Czech Republic international could not deny the Frenchman in the final minutes when he exchanged passes with Santon before drilling a sweet drive past Cech to win it.