Taylor's stunning 29th-minute volley ultimately edged the tightest of contests in front of a season's best crowd of 50,671 to take Alan Pardew's side, for a few hours at least, ahead of Manchester United.
The victory ensured they matched their best unbeaten openings to a campaign in 1950-51 and 1994-95.
However, it came at a cost as Yohan Cabaye and Sylvain Marveaux joined Cheik Tiote on the injured list with daunting trips to both Manchester clubs to come after the international break.
Everton left St James' Park knowing they probably deserved to be doing so with something to show for their efforts having given as good as they got, particularly in a nerve-jangling second half for the Toon Army.
However, they were never able to claw back the advantage they had handed their hosts through John Heitinga's 12th-minute own goal and Taylor's rocket despite giving themselves hope with Jack Rodwell's header in first-half injury-time.
Newcastle went into the game knowing exactly what the rewards for victory would be and defending a proud record at St James' Park.
Only Everton had won on Tyneside this calendar year, a run of 14 games, and Pardew had admitted before the game that a point would represent a creditable return.
However, as the clock ticked towards the half-hour mark, his side found themselves two goals to the good, although even the most blinkered of fans would have to admit that scoreline slightly flattered them.
That said, the quality which led to Tim Howard's defences being breached on both occasions was worthy of the outcome and while it is strikers Demba Ba and Leon Best who have done much of the damage so far this season, the source this time was somewhat different.
The game was 12 minutes old when Steven Taylor laid the ball into Danny Guthrie, once again deputising for the injured Tiote, and he fed it out to full-back Danny Simpson in space down the right.
Simpson's cross looked tailor-made for Best in the middle and Heitinga had little option but to try to cut it out, but with disastrous results as he could only turn it past Howard and into his own net.
But in an even encounter, the visitors had opportunities to get themselves back on level terms Rodwell forcing a 23rd-minute save from Tim Krul, who clutched Leon Osman's shot to his midriff seconds later, while former Magpies Louis Saha shot wastefully wide with 25 minutes gone.
However, Newcastle extended their lead in spectacular style four minutes later.
Rodwell's clearing header fell to Ryan Taylor wide on the left and he teed the ball up before thumping a dipping volley over Howard an in off the underside of the crossbar.
With Royston Drenthe impressive in a roaming role behind Saha, Everton tried to work their way back into the game and might have reduced the deficit with 13 minutes remaining, only for Saha's skidding shot to come back off the foot of the post.
Ryan Taylor bounced a 34th-minute cross off Howard's crossbar as played switched rapidly from end to end, but the Magpies were left kicking themselves when the visitors grabbed a lifeline in injury time with Rodwell heading firmly home from Drenthe's near-post corner.
The sides returned knowing the next goal could prove vital, and both might have claimed it in an eventful start to the half.
Saha's appeals for a penalty after his shot was deflected wide - replays suggested it may have been so off substitute Gosling's arm - went unanswered at one end, and Sammy Ameobi, on for the injured Marveaux, scuffed a shot across the face of goal after breaking from halfway.
Substitute Tim Cahill forced Krul to dive to his left to save on the hour and Ameobi skied a left-foot volley high over seconds later.
But Newcastle were having to defend deep and in numbers, and it was significant that Ba and then Best were the men to head clear inside their own penalty area from Leighton Baines and Seamus Coleman in quick succession in the 63rd minute.
Everton threw everything they had at the Magpies as the clock ran down with the home side retreating towards Krul at an alarming rate.
However, they were unable to make the breakthrough and left Tyneside empty-handed.