Aberdeen and Dundee played out a goalless first half at Pittodrie.
Dundee's hopes of making a top-six spot were dealt a bitter blow before the kick-off with striker Claudio Caniggia calling off with a hamstring injury.
His place was taken by Fabian Caballero.
Dundee pressed forward from the start and were almost rewarded in six minutes when Caballero found himself clear inside the area.
His lob from 12 yards beat Esson but was headed clear.
Aberdeen's response was immediate, Derek Young was sent free on the right, his driven cross from the edge of the area being cleared.
With 14 minutes played Aberdeen missed the best chance yet. Robbie Winters brilliantly played in midweek hat-trick hero Arild Stavrum, but shot narrowly past the upright.
Rae picked out Sara and he advanced into the area before unleashing a tremendous shot which crashed off the crossbar and away to safety.
Confusion in the Dundee rearguard between Coyne and Langfield almost let Derek Young in on goal but the ball was eventually scrambled away to safety.
Good interplay between Sara and Caballero in 36 minutes almost led to the breakthrough Dundee so desperately wanted but Sara was closed down by the Dons' defence as he was about to shoot.
Urged on by a large travelling support, Dundee continued to hold the upper hand without being able to make the most of the few chances that were in the game.