Nolan put the home side 2-0 ahead within 34 minutes and completed his treble 15 minutes from time, after Ameobi had helped himself to two goals, the first of them from the penalty spot.
It was the first hat-trick in the fixture since Peter Beardsley achieved the feat for Newcastle in January 1985.
Sunderland, who had former Magpies defender Titus Bramble sent off for an ill-judged challenge on Andy Carroll in the 53rd minute, were never at the races on a day when their promoted neighbours won at St James' Park for the first time in five attempts.
Darren Bent's last-minute strike was no consolation for the travelling fans, many of whom had already left.
It proved a sweet afternoon for Chris Hughton following a week during which speculation over his future at the club reached fever pitch.
The 51-year-old was serenaded by the delighted home contingent in a crowd of 51,988 as his side completely outplayed their most bitter rivals, who rarely troubled goalkeeper Tim Krul until Bent's late effort, despite Geordie manager Steve Bruce sending on record signing Asamoah Gyan before half-time to add firepower.
Sunderland had conceded only seven goals in their first nine Premier League games, but were repeatedly torn apart by a committed Magpies side even before Bramble's premature departure.
The Black Cats arrived on Tyneside in an optimistic mood on the back of a seven-game unbeaten Premier League run to meet a side which had not won on their own pitch in four attempts.
But Sunderland's goals-against total was to rise significantly inside a rousing opening 45 minutes during which Newcastle took the game by the scruff of the neck.
The Magpies were on the front foot from the off as the game started at a lively pace, and they steadily built momentum before exploding into life with 24 minutes gone.
It took a fine reaction save from Simon Mignolet to keep out Andy Carroll's bullet header, and the Belgian had to be equally alert two minutes later to claw Joey Barton's stinging drive away from the bottom corner.
But the deadlock was finally broken from the resulting corner when central defender Mike Williamson got up well to head down Barton's corner and Nolan sent the ball into the roof of the net with an acrobatic overhead kick.
The noise level at St James' Park reached ear-splitting levels as Nolan was mobbed by his team-mates, and it was to get much, much better for the home fans before the half-time whistle sounded.
Newcastle increased their lead within eight minutes when Carroll's scuffed volley fell perfectly for the criminally unmarked Nolan, who controlled before slipping the ball past the advancing Mignolet.
Bruce's game plan was simply not working, with lone striker Bent almost redundant, and the manager made his tactical move five minutes before the break when he sent on £13million-plus man Gyan in place of Ahmed Elmohamady and switched to a 4-4-2 formation.
But before the new arrival could make an impact, his side fell further behind after Nedum Onuoha's clumsy injury-time challenge on Jonas Gutierrez prompted referee Phil Dowd to point to the spot.
Ameobi, who converted a penalty in the corresponding fixture two seasons ago, repeated the feat to pile the pressure on Bruce and his players.
Sunderland's reshuffle had seen Steed Malbranque drop into a midfield four and Jordan Henderson move out to the right, and while that gave them a better shape, they caused few problems for their hosts in the opening minutes of the second half.
Their woes deepened with 53 minutes gone when in his eagerness to prevent Carroll from racing in on goal, Bramble launched himself into a desperate challenge which sent the striker sprawling, and was punished with a straight red card.
Carroll sent a towering header over the bar two minutes later with the visitors rocking, and Bruce introduced Kieran Richardson as a replacement for Danny Welbeck with things going from bad to worse.
Krul, who had been a virtual spectator for much of the game, had to get down well to turn away Phil Bardsley's 65th-minute strike, but the Magpies were coasting to victory.
They increased their lead with 20 minutes remaining when Carroll's powerful header came back off the crossbar and Ameobi rifled home spectacularly.
There was worse to come five minutes later when Nolan met Ameobi's flick-on two yards out to complete his hat-trick, and Bent's last-minute strike repaired none of the damage inflicted on the demoralised visitors.