Naysmith, who joined the Toffees mid-week from Hearts in a £1.75 million deal, rampaged down the left on 80 minutes before crossing for Campbell to slide home the winner at the back post.
It was a rare display of invention in a game that for the most part was scrappy, despite the return of Paul Gascoigne to the ground where he began his career 16 years ago.
Gazza received a hero‚ÇÖs reception from the Toon faithful, but couldn‚ÇÖt produce anything but the briefest glimpses of the genius that secured his place in football folklore.
Instead it was Everton‚ÇÖs tireless, but rather uninspiring team display that gave boss Walter Smith his first three points since September 9 and a first clean sheet in ten games.
In contrast, Newcastle were left ruing a missed opportunity to hang onto the coat tails of Manchester United after overall enjoying the best chances of the afternoon.
Warren Barton bolstered Newcastle‚ÇÖs starting line-up, while Abel Xavier ‚Çô making only his second appearance of the season - and new boy Israeli international Idan Tal both started for Everton.
Everton succeeded in weathering the anticipated early storm ‚Çô which turned out to be little more than a passing breeze - but couldn‚ÇÖt carve out any chances until Alex Nyarko picked up the ball 30-yards out and drove straight at Shay Given.
Had Didier Domi been sent off for chopping down Thomas Gravesen early on - it might have been the catalyst the game needed ‚Çô but he only saw yellow.
Only occasionally did the midfield battle break into calculated attacks, and it was the home side who sporadically threatened.
Bruce Dyer should have given the home side the lead, but even with a prodigious leap, was still a couple of inches under Kevin Gallacher‚ÇÖs cross and only succeeded in heading over from five yards when unmarked.
The right was also Everton‚ÇÖs most productive outlet, and United old boy Steve Watson had a reasonable penalty shout turned down when his drag-back from that flank seemed to be blocked by a rogue hand.
More controversy followed when Michael Ball scythed down Gary Speed after Gerard had parried a fierce Alan Shearer 25-yard free-kick, but the Under-21 international got away with a yellow card.
The game needed someone to take it by the scruff of the neck and pacy Naysmith duly obliged on debut to seal three prized points.
