The ex-Scottish champions, recovering from a financial crisis, needed a last-minute equaliser from Andy Little in front of 4,500 fans at Balmoor stadium on the north-east coast of Scotland.
It was Rangers' first league match outside the top flight of Scottish football.
The club went into administration in February before a takeover in June, and were demoted from the Scottish Premier League to the third division - the bottom of the country's footballing pyramid - after a meeting of Scottish Football League clubs last month.
Rangers are clear favourites to win the third division, but manager Ally McCoist said Saturday's result was a warning to his players. "If our boys at any time thought this was going to be a cakewalk, they know where they are now," he told Sky Sports.
"Obviously them scoring late on, [I'm] probably relieved to get a point after the game. I thought we defended appallingly, to be honest."
McCoist's side got a fine start when Barry McKay put them in front with a cool finish on 26 minutes.
