Scott Arfield was on hand with that sensational double, with Gers earlier leading through a Fashion Jr strike before the Dons turned the game around.
The manager was proud of his players at the end – but warned they still have to find a much higher level of performance.
He told RangersTV: "It's 10 out of 10 for mentality. I thought I would make four subs late in the game and to change the system to try and free people up a little bit and Scotty Arfield does what Scotty Arfield does - two runs into the box to arrive and score.
"Malik Tillman, again, for the third goal, a little bit of magic. We might have had a penalty thrown in and I thought at times in the first half we looked dominant - we scored a good goal and we should have gone in at half-time 1-0 up and it was a poor moment that gave away the free-kick that led to the goal, and then we didn't start the second half and I had to make the changes to shake it up.
"So it is 10 out of 10 for mentality and character, but maybe five out of 10 for performance - we are a work in progress."
Beale hopes the manner of the comeback can inspire his players going forward, and he added: "You would like to think they would believe in themselves and believe in any moment of the game if we can continue to play how we want to play, we will create chances and score.
"There was a little bit of an incident in the game second half which allowed me to get them back in and to tell them to calm down and to just keep passing the ball and just keep running, and something would happen.
"And it did - Ryan had a shot from distance, Scotty just being optimistic, gets in there and then Malik, fantastic down the right wing digs out a cross and we managed to find a winner through Scotty Arfield getting his second on the night.
"It would have been very, very harsh had we lost, so I am naturally delighted that we have won."
It’s now a quick turnaround to Ross County in Dingwall on Friday night, and the manager explained: "We will have a nice chat tomorrow. There will be some changes to the starting line-up on Friday to freshen things up and one or two faces coming in to the team and it is their opportunity.
"They have been waiting in the background like Scotty tonight coming on. Scotty has been training ever so well and he waited for his chance and he took it.
"We know we have got a big support up in that part of the country and we are delighted to be going back and seeing our fans up there before Christmas and let's try to make it three from three on Friday."
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