Rangers 1-2 Aberdeen
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Aberdeen secured their first win at Ibrox since 1991 as Rangers lost their final home match of the season.
Graeme Shinnie drove through the home defence to slot in the Dons' opener.
Goalkeeper Wes Foderingham denied Ash Taylor, Niall McGinn and Adam Rooney as the visitors continued to threaten and Ryan Christie headed their second.
Substitute Martyn Waghorn replied for the hosts before the Dons had Jayden Stockley sent off for two bookings but Aberdeen saw out victory.
Debutant Aidan Wilson (left) could not prevent Shinnie getting the opener
They had all but secured the runners-up spot but the result at Ibrox ensured the Pittodrie side will finish second to Premiership winners Celtic for the third season running.
Dons boss Derek McInnes had said before the match his former club Rangers "should probably be embarrassed that they've not finished second" owing to the Glasgow side's greater financial clout.
And Aberdeen's determination to end their long wait for a victory at Ibrox was evident early on as Shinnie stole possession, evaded defenders and fired low past Foderingham.
The visitors may have added to their lead in the opening period. Christie claimed he was impeded in the box by Rangers' teenage debutant defender Aidan Wilson and efforts by Taylor and Rooney were blocked by Foderingham before McGinn's free-kick was also saved.
Joe Garner was off target with a couple of efforts as Rangers tried to draw level and Barrie McKay fired wide of Joe Lewis's goal.
Aberdeen's win over Rangers was their first at Ibrox since 1991
The hosts had been forced into a first-half change when full-back Lee Hodson made way for Myles Beerman and manager Pedro Caixinha sent on forward Waghorn in place of Joe Dodoo at the break.
But Aberdeen's dominance continued with McGinn and Rooney forcing saves from Foderingham in quick succession.
Then, on-loan Celtic midfielder Christie looped a header into the net from close range following Rooney's headed knock down.
Rangers were soon back in the match, however, with Josh Windass slipping the ball to Waghorn to stroke past Lewis.
But an equaliser never materialised, despite chances for Garner and McKay - the latter also having an unsuccessful penalty claim - and Rooney's replacement Stockley being dismissed in the final minute of regulation time.
Waghorn's goal gave Rangers hope but Aberdeen held out