Kilmarnock substitute Jamie Fowler came off the bench to score once and set up Andy McLaren for another goal in the first half at Aberdeen.
But the Dons managed to pull back a goal a minute from the break through striker Arild Stavrum who tapped in from close range.
Aberdeen should have taken the lead in the first minute in their home match against Kilmarnock.
Robbie Winters raced down the left, and his cross into the middle was met by Stavrum who misdirected his header.
The ball fell to Alex di Rocco, but his shot from eight yards went high over the Kilmarnock bar.
The visitors replied immediately, and a cross from Alan Mahood was turned away for a corner by Kevin McNaughton with the Dons defence in trouble.
In the fifth minute the Dons carved open the Kilmarnock defence.
Eion Jess turned inside Kilmarnock defender Sean Hessey, but his shot from 16 yards was well saved by goalkeeper Gordon Marshall.
At the other end Mahood came close for the visitors with a curling shot from the edge of the box which went narrowly past Ryan Esson's left-hand post.
The game seemed to be settling into something of a stalemate when, against the run of play, the visitors took the lead.
Dargo raced down the right and his cutback from the by-line found substitute Fowler at the edge of the Aberdeen box.
Fowler, who had only been on the park for five minutes after an injury to Ally Mitchell, stabbed the ball to McLaren 16 yards from goal.
The Killie midfielder looked up and drove a glorious shot past goalkeeper Esson.
A minute later the home fans were further stunned when Fowler made it 2-0, racing onto a Christophe Cocard pass, with the Aberdeen defence sleeping and easily slotting past Esson.
To their credit, Aberdeen kept fighting and were rewarded a minute from the break when Stavrum pulled a goal back, tapping in from close range with the Kilmarnock defence claiming offside.