The Magpies, a club in turmoil when they were relegated 12 months ago, made short work of the second tier and became the fourth side to rack up 100 points or more in a season after romping to the title.
Peter Lovenkrands' neat 71st-minute strike ensured they signed off their brief stint outside the top flight with a win.
The bare-chested hordes who had made the trip south were in party mood as they celebrated their return to the Premier League.
But the carnival atmosphere had not rubbed off on referee Darren Deadman, who showed Rangers' former Newcastle defender Peter Ramage a straight red card seconds after the break.
The first half was an uninspiring affair, with both sets of players in end-of-season mode on a slippy pitch which had to pass a morning inspection.
Newcastle's ex-Hoops winger Wayne Routledge tried to lift the tedium with a sharp turn and shot but his effort flew straight at home goalkeeper Radek Cerny.
At the other end, Akos Buzsaky blazed a decent chance high over the crossbar, before stand-in goalkeeper Tim Krul made a meal of holding onto Alejandro Faurlin's drive.
There was little else to get excited about until seconds before the interval when Jay Simpson raced onto Faurlin's fine long pass, but his touch let him down and Krul was able to gather.
The second half was just 15 seconds old when Ameobi charged past Ramage and was hauled down.
Deadman decided the defender was the last man and Ramage cut a disconsolate figure as he trudged off.
The dismissal seemed to spark Rangers into life and they had the ball in the net in the 55th minute, but Tamas Priskin was marginally offside when he collected Simpson's pass and chipped Krul.
But it was the visitors who eventually made the breakthrough with a goal of Premier League quality.
Joey Barton's pass split the Rangers defence and Lovenkrands, who had been on the pitch for 17 minutes, beat the offside trap before lofting his finish over Cerny and into an empty net.
Simpson could have spoiled the party and hauled Rangers level when he scampered clear again, but Krul stayed big to block his shot and the Magpies held on to chalk up their 30th win of a successful campaign.