Gouffran's 68th-minute diving header and Remy's late strike, his sixth goal of the season, settled a game which blossomed from modest beginnings into an end-to-end encounter.
Indeed, had it not been for keeper Petr Cech, who had earlier made second-half saves from Moussa Sissoko and Gouffran, the Magpies might have gleaned more reward than the 2-0 win with which they emerged from a testing afternoon.
But while manager Alan Pardew will have been delighted with a performance which started out as a backs-to-the-wall battle and ended in a toe-to-toe slugging match, opposite number Jose Mourinho was left to reflect upon a toothless display from his all-stars.
Chelsea dominated for long periods in front of a packed house of 51,674, but having hit the bar twice within seconds early in the game, did not call upon keeper Tim Krul until 10 minutes from time on a day when victory would have seen them leapfrog Arsenal for a few hours at least.
On a miserably cold and wet Tyneside afternoon, the fare on offer initially did little to lift the mood as an attritional game unfolded.
Chelsea, as befits a team installed as early favourites to lift the title, started confidently and pinned their hosts back for long periods with Eden Hazard leading the home defence a merry dance.
With Fabricio Coloccini and Steven Taylor still injured, Pardew had little choice but to field Mike Williamson and Mapou Yanga-Mbiwa at the heart of his rearguard, and just how the Magpies managed to survive an error-strewn opening to the game only they will know.
A series of miskicks and misdirected headers, thankfully for the pair, dropped fortuitously and allowed Newcastle to dig themselves out of trouble.
However, the inability of Pardew's men to retain possession for anything other than a few seconds left them constantly under pressure with Hazard and Oscar capitalising on their profligacy.
They had to ride their luck at times with the crossbar coming to Krul's rescue twice within seconds in the 13th minutes, when Chelsea skipper John Terry climbed highest to head Juan Mata's corner against the woodwork before Fernando Torres' deflected follow-up was repelled in similar fashion.
But for all their pressure, the visitors were unable to test Krul further and as they gradually found their feet, the Magpies began to compete.
Initially, they relied upon the long ball up to striker Shola Ameobi, preferred to Hatem Ben Arfa, with decidedly limited success.
But as they grew in confidence, both Yohan Cabaye and Sissoko tested Cech after more enterprising build-up play, and they headed for the dressing room at half-time satisfied with their opening 45 minutes, but knowing much, much more would be required after the break to secure tangible reward.
As a result, they resumed on the front foot and attempted to attack Chelsea, although their wastefulness in possession continued to court disaster.
Pardew was forced to make a change with 53 minutes gone when in-form skipper Cheick Tiote limped off and was replaced by Vurnon Anita.
In their efforts to take the game to the visitors, Newcastle piled forward in numbers, in the process leaving space in behind which the Blues attempted to exploit in a series of counter-attacks.
But it was the Magpies who went close to the opening goal twice within seconds when Cech made a fine save from Sissoko's skidding 60th-minute drive after he had been played in by Mathieu Debuchy and Remy volleyed straight at the keeper from Ameobi's knock-down.
Buoyed by the growing momentum, Pardew sent on Papiss Cisse for Ameobi as Willian and Samuel Eto'o replaced Oscar and Torres, but it was Gouffran who tested Cech at the foot of his near post after cutting inside Branislav Ivanovic with 25 minutes remaining.
But the Frenchman was not to be denied and he got his reward three minutes later in spectacular style.
Cabaye's curling free-kick caused all kinds of problems for the Chelsea defence, but Gouffran read it perfectly to dive and power a header past Cech.
Mourinho swiftly replaced Frank Lampard with Andre Schurrle, but the home side might have increased their lead with 72 minutes gone when Sissoko and Remy carved a path through the blue shirts before the latter saw his shot block by the sliding Terry.
However, Krul had to be at his best 10 minutes from time to beat away Willian's snapshot with an instinctive save, and Debuchy was on hand to block Eto'o's follow-up to ensure the points remained on Tyneside.
Hazard fired inches wide with four minutes remaining, but Remy made sure at the death when he thumped Anita's pull-back past the helpless Cech.