But a goal from Jon Gallagher – making amends for his part in the Light Blues' opener – just before the break restored some much-needed belief and they levelled soon after the change of ends as Steven Gerrard saw his side's intensity levels fall off a cliff.
The Ibrox boss insisted before the match his side would not take their eye off the ball before Sunday's Betfred Cup final with Celtic.
But it is they who appear to have blinked first in their neck-and-neck title race, with the Hoops edging two points ahead at the top of the Ladbrokes Premiership.
Borna Barisic was a surprise absentee for the visitors as Jon Flanagan came back in for his first start since September's Old Firm defeat and there will be some concern now about the Croatian's availability for Hampden.
Derek McInnes admitted over the weekend that Gers were a better team with better players than his side – and his concern was evident as he named a starting line-up that included six recognised defenders.
And the hosts looked stricken with fear early on. Gers were allowed to send cross after cross into the box as the Dons continually invited pressure.
They were only going to get away with that kind of sloppiness for so long and Rangers finally capitalised after 18 minutes.
Gallagher's touch deserted him and Joe Aribo was on him in an instant. He drove forward before picking his moment to lay off to James Tavernier, whose low cross from the right was expertly steered home by Arfield.
That setback only enraged a home support already simmering even further. Lewis Ferguson tried to get them back onside by trying something spectacular but Allan McGregor simply took a couple of steps back before plucking the midfielder's 35-yard attempted lob into his chest.
Instead, it was the travelling faithful who were celebrating again as Aberdeen served up another goal to Rangers on the half-hour mark.
Zak Vyner was under no pressure on half-way yet still managed to gift possession straight to Jack. Joe Lewis then failed to deal with Morelos' fairly routine strike, letting it squirm loose for Jack to gobble up to the dismay of his former club's supporters.
It was looking like another goal for Gerrard's team would put the game to bed before half-time.
But out of nothing the hosts grabbed a lifeline. James Wilson and Sam Cosgrove combined on the edge of the Rangers box before Gallagher took over, going round McGregor before hooking the ball past Tavernier on the line.
It was Rangers' turn to look shaky as the action resumed after the break. Jack was robbed just outside his box and had McGregor to thank as he denied Cosgrove.
But Gerrard's team did not heed that warning and found themselves level after 48 minutes.
Kent switched off as Ferguson collected a throw-in then hooked the ball into the six-yard box for Cosgrove. Aberdeen's top-scorer saw his attempt to bundle home blocked but the bounce was kind as it looped to Considine to ram home at the back post.
It was an incredible turnaround. Where the Light Blues had been slick in the first period they were now ragged and they should have fallen behind with 20 minutes left but Cosgrove failed to nod home from point-blank range.
Gers were given a free-kick soon after when Ferguson tripped Morelos but replays showed the collision was inside Aberdeen's box.
Tavernier sent the set-piece into the wall to add to Gerrard's annoyance before seeing Lewis push away another late on.