Derek McInnes' team are the closest challengers to the runaway leaders but they could only claim a 1-1 draw at Dingwall and finished with 10 men.
Melvin De Leeuw headed the hosts in front in the 35th minute and Yoann Arquin should have doubled the advantage before the break.
Aberdeen responded impressively, striking the post and crossbar on three occasions before Adam Rooney netted an eighth goal in 11 appearances since joining from Oldham Athletic in January.
Both teams pushed for an elusive winner, Andrew Considine receiving his red card for a professional foul on County's Graham Carey, and all eyes will now turn to Celtic.
Should Partick pull off an improbable triumph, they will pull clear of St Mirren in the relegation play-off spot after the latter went down 1-0 at home to St Johnstone.
Steven MacLean volleyed the only goal of the game six minutes before half-time from David Wotherspoon's cross.
St Johnstone are already assured of a top-six berth when the Premiership split occurs after 33 matches.
‘I had to prove myself to the Nottingham Forest fans after crossing the divide from Derby, but it didn’t take too long – I showed I was there to score goals’: Ex-Forest striker reveals how tough start at City Ground quickly changed
The games Arsenal star Bukayo Saka is expected to miss following his painful injury setback
