Lee McCulloch gave the hosts the lead after just five minutes, but Alan Pardew's side, which featured Yohan Cabaye, Hatem Ben Arfa and Papiss Cisse, salvaged a draw
Ameobi found the leveller in the dying stages of a frenetic encounter after Lee McCulloch had put the Scottish side in front from the penalty spot after five minutes.
Newcastle's starting XI did not feature new loan signing Loic Remy, but the likes of Yohan Cabaye, Hatem Ben Arfa and Papiss Cisse were all involved as manager Alan Pardew fielded a strong side.
However, it was the hosts who took the lead early, McCulloch converting from 12 yards after Fabricio Coloccini had felled Nicky Clark.
The visitors responded well, with Ben Arfa curling an effort over the bar before Mathieu Debuchy saw a volley well saved by Rangers goalkeeper Cammy Bell.
Newcastle continued to enjoy the majority of the possession in the first half, but they found no reward for their efforts as Cabaye, Cisse and Ben Arfa all went close, but Rangers made it to the interval with their slender lead still intact.
Pardew made two changes at the break, with Ben Arfa and goalkeeper Tim Krul replaced by Yoan Gouffran and Rob Elliot.
Again it was Ally McCoist's men who started the half the better, however, with Clark forcing an excellent save from Elliot just three minutes into the second period.
Newcastle made numerous changes throughout the half, but that did not affect the pattern of the game, with a strong Rangers defence responding well against concerted pressure from Pardew's charges.
Ameobi looked to have wasted the best chance of the second half after 78 minutes when he headed wide from a right-wing cross from Gouffran, but he atoned for that miss in the final minutes, guiding a lofted finish over Bell after good work from younger brother Sammy to ensure that the contest ended all square.