Looking a good two yards offside from an Emre free-kick, Ameobi checked he was given the green light by the assistant referee before beating Tim Howard.
Furious Everton replied through Tim Cahill who headed his 20th goal for the Goodison Park club - ten of which have come from his head.
That all happened in the first half after which Titus Bramble saw red for two yellow cards from referee Steve Bennett.
Three minutes later Bramble was followed down the tunnel by Everton full-back Tony Hibbert after he too was twice yellow carded.
Bennett also booked four other players including United's Emre who has now been yellow carded in three of Newcastle's last four Premiership games.
Worryingly for Newcastle boss Glenn Roeder, his side have now played three home games this season and lost the lead on each occasion as they have now collected a full set of results - a win, draw and loss.
Newcastle now head to Old Trafford next Sunday without both Bramble and Celestine Babyaro who will complete the second game of a three-match ban, although they are both available for Thursday's UEFA Cup tie with Levadia Tallinn at St James' Park.
Newcastle started well and an early Emre corner broke to Charles N'Zogbia who lashed his effort high over the bar and James Milner then drove wide when picking up a poor Lee Carsley clearance.
Milner then crossed from the right and Ameobi's glancing header struck Joseph Yobo and Howard held onto the deflection just under the bar.
Newcastle took the lead after 14 minutes. Everton charged out as Emre swung in his left-wing kick and Ameobi checked that the assistant was allowing him to play on before putting away his fourth goal of the season and second in the Premiership.
Cahill powered a drive away as Everton responded and Joleon Lescott should have done better when unmarked but glanced Mikel Arteta's free-kick wide.
Howard, at full stretch, kept out a Scott Parker lob while at the other end another Arteta cross was headed wide by Carsley.
The equaliser arrived five minutes before the break. A clearance fell to Phil Neville who astutely sprayed the ball wide right to Arteta whose deep cross was nodded in at the far post by Cahill.
Booked for a late lunge on Andy Johnson in the first half, Bramble could have few complaints when clattering into Leon Osman from behind on the edge of the box after 75 minutes.
Referee Bennett then balanced it up when Hibbert followed soon afterwards for clattering into Antoine Sibierski – his second yellow in 16 minutes.
A poor Craig Moore pass then let Osman clear but Steve Harper made an excellent save and not long afterwards Stephen Carr made a crucial near post clearance as Johnson was about to pounce.