Lee McCulloch gave Rangers the lead from the penalty spot with four minutes on the clock after Fabricio Coloccini felled Nicky Clark.
Hatem Ben Arfa almost restored immediate parity but his curler dipped just the wrong side of the post.
The Magpies piled on the pressure as the half drew to a close with Yohan Cabaye and Papiss Cisse both passing up presentable opportunities as Rangers took their lead to the interval.
Ameobi then missed a gilt-edged chances in the 78th minute when he headed wide from close range but he made up for that miss in the final minute when he lifted the ball over Cammy Bell to level things.
Nicolas Anelka scored a hat-trick as West Brom recorded a 6-0 friendly victory over Cork City.
Graham Dorrans was also amongst the goals as he scored twice and Shane Long netted a goal against his former club.
Anelka chested home a Dorrans cross after 25 minutes to open the scoring before Dorrans fired home a left-footed shot from the edge of the box on the stroke of half-time.
Summer signing Anelka made it three two minutes after the restart, before former Cork City man Long added the fourth a minute later.
Anelka completed his hat-trick after 63 minutes with a smart finish.
The home faithful thought they may have had a consolation to cheer but Andy O'Connell missed a penalty after Goran Popov had felled Rob Lehane.
And Dorrans raced on to a through ball with 17 minutes to play to finish off the scoring.
A second-half strike from Emidio Rafael condemned West Ham to their second defeat of pre-season against Braga.
West Ham created plenty but failed to breach the Braga goal and a firmly struck effort from the full-back was enough to secure the win for the Portuguese side.