They were reduced to 10 men on the hour mark when captain Mark Kerr was shown a second yellow card for a challenge on Steven Naismith.
Rangers threw everything at the Dons until the final whistle but the home side managed to withstand the pressure to earn a hard-fought victory.
Madjid Bougherra again started on the bench for Rangers as Walter Smith kept faith with 17-year-old Danny Wilson. The Ibrox side did make two changes with John Fleck and Naismith replacing Kenny Miller and Kevin Thomson who both dropped to the bench.
Aberdeen also made two changes with Chris Maguire coming back from suspension to replace Gary McDonald who missed out after being red-carded against Motherwell last weekend.
Derek Young also returned to the starting 11 with Andrew Considine missing out.
Dons defender Zander Diamond was a surprise inclusion on the bench after a lengthy lay-off with an ankle injury.
Mark McGhee's men were dealt an early blow when Jerel Ifil limped out of the warm-up and had to be replaced by Italian defender Davide Grassi.
Rangers gave the makeshift Aberdeen rearguard, with a central defensive pairing of Richard Foster and Charlie Mulgrew, an early warning when Lee McCulloch headed wide from a Fleck corner.
The home side also started brightly with Maguire volleying over the bar followed by a mazy Peter Pawlett run that ended with the teenager's shot being deflected wide for a fruitless corner.
Aberdeen's positive start was rewarded after 17 minutes when Paton twisted past Steven Whittaker to drive a low cross into the box that was prodded home by Miller for his third goal of the season.
Rangers could have restored parity after 26 minutes when Kris Boyd skipped past Foster before unleashing a volleyed shot-cum-cross that was headed over by Kyle Lafferty with the goal gaping.
The away support were screaming for a penalty on the half hour when Whittaker fell under pressure from Maguire but referee Craig Thomson waved play on.
The lack of height in the home defence was encouraging Rangers to take a direct approach and a hopeful kick up field by Allan McGregor allowed Boyd to outmuscle Foster but Jamie Langfield palmed away the striker's effort.
Foster then rescued the Reds when he got his body in front of Boyd's goalbound left-footed volley as the visitors were denied an equaliser just before the break.
The ineffective Kyle Lafferty was replaced at half-time by Miller and the substitute had an early chance to make an impact but his weak shot was easily gathered by Langfield.
The Dons had a great opportunity to double their advantage when Sasa Papac was booked for upending the lively Pawlett on the edge of the box. But the Bosnian made amends by clearing Mulgrew's free-kick, which took a wicked deflection, off the line.
The Dons were reduced to 10 men on the hour when Kerr, who had already been booked for a foul on Naismith after 49 minutes, was given a second yellow for another challenge on the same player.
Stuart Duff came on for Maguire a couple of minutes later as the home side readjusted their formation to cope with their numerical disadvantage.
The visitors, who were struggling to break down a battling Dons defence, introduced Bougherra for Whittaker with 14 minutes left to play.
The home side were camped in their own half with little respite in the final stages but were working hard to withstand the incessant pressure.
The impressive Paton was withdrawn for Darren Mackie in the closing stages as the Dons tried to hold on for a famous victory.
Mulgrew managed to prevent substitute Nacho Novo netting with a last-ditch clearance before Boyd was denied by Langfield as the hard working Dons held on for all three points.