Rangers huffed and puffed against the Dons but could find no way through to book their place in the match on December 2.
The superb, as ever, support of 32,000 Bears inside the National Stadium made one hell of a racket as the teams emerged, with a fantastic display of the Saltire and Union Flag being held up by fans in the West Stand.
Inside the first minute, Gers were dealt a blow with Ovie Ejaria booked for bringing Lewis Ferguson down 25-yards from goal following some slack play from Joe Worrall. The resultant free-kick saw Niall McGinn force Allan McGregor to push the ball behind for a corner.
Gers defended that well, but as Daniel Candeias looked to break with the ball, he was scythed down by Graeme Shinnie to make it a booking apiece in the opening two minutes.
It was certainly a lively opening to the game, and Umar Sadiq came close to opening the scoring when he powerfully met a Tavernier free-kick at the back post with his head, but under pressure from Scott McKenna, he could only put his effort just over the bar.
McGinn then found himself with another opening after Scott Wright ghosted by Jon Flanagan out on the left, but the Northern Irishman found only the track behind the goal with a lofted effort.
Candeias was really growing into the game, and after beating McKenna to a through ball from Ryan Jack, he skinned the Scotland defender with some sensational skill, found Ejaria on the edge of the box, but he could only shoot just wide with a curling effort.
Sadiq then did well to chest a Flanagan ball into the path of the onrushing Ryan Jack, and he came within inches of netting the opening goal against his former club while Worral had a wild effort at goal after Sadiq again impressed in bringing the ball down, this time from another Tavernier free-kick,
A serious-looking injury to Aberdeen’s Andy Considine necessitated eight minutes of stoppage-time at the end of the first half before referee John Beaton brought both sets of players off for Steven Gerrard and Derek McInnes to deliver their respective messages.
It took the second half a while to ignite, but on 53 minutes, Gers all of a sudden laid siege to the Aberdeen goal. An Ejaria shot was well-blocked before the ball broke left for Ryan Kent to flash a tremendous ball across the face of goal that was just begging to tapped home.
Connor Goldson then came over all Madjid Bougherra with a superb surging run from defence to the edge of the 18-yard box where McKenna hacked him down. Tavernier’s resultant free-kick was over the bar, while minutes later, the captain had a corner met on the penalty spot by the boot of Lassana Coulibaly, but he couldn’t quite turn the ball home.
A well-read interception from Candeais and a fine run from the Portuguese released Kent to burst into the box from the left before McKenna came across to deflect his effort on goal behind.
The half had belonged to Rangers, but in the 79th minute, Aberdeen grabbed the lead. McGinn’s corner into the six-yard box was met by the head of Lewis Ferguson, and he powered the ball beyond Allan McGregor.
Gerrard responded immediately by bringing on Scott Arfield and Glenn Middleton for Daniel Candeias and Ryan Jack.
Arfield nodded a Kent cross wide in the final minute of normal time, but Aberdeen held firm to secure victory.
RANGERS: McGregor; Tavernier, Goldson, Worrall, Flanagan; Jack (Middleton, 82), Coulibaly, Ejaria; Candeias (Arfield, 82) Kent, Sadiq.
SUBS: Foderingham, Halliday, Rossiter, Katic, Grezda.
ABERDEEN: Lewis, Logan, Shinnie, Considine (Lowe, 36), McKenna, Wilson (Ball, 86), McGinn, Mackay-Steven, Wright (May, 60), Devlin, Ferguson,
SUBS: Cerny, Gleeson, Cosgrove, McLennan..
REFEREE: Mr John Beaton
ATTENDANCE: 46, 186