Dodds scored after 51 and 69 minutes Tuesday to put Aberdeen into the final on Nov. 26 against either Dundee or Airdrie, who were set to meet in the other semifinal in Perth on Wednesday.
Aberdeen had to endure an anxious finish after Russian marksman Oleg Salenko pulled a goal back in the 85th minute, but it hung on for the upset win.
It represents a remarkable transformation in the fortunes of Premier Division Aberdeen, which escaped from relegation at the end of last season only through a playoff.
Aberdeen took the lead when Salenko lost possession inside its half and Eoin Jess went on a surging, 60-meter run. He slipped his pass to Dodds, who got a deflection off a Rangers' defender before squeezing the ball home.
Dodds got his second goal when he found himself in space on the far post to head home.
In English play, two strokes of quality from Dutchman Dennis Bergkamp enabled Premier League club Arsenal to brush aside first division Barnsley 3-0 in their League Cup match.
Bergkamp, the ?7.5 million ($11.85 million) signing, silenced the majority of the 18,000 home crowd with a searing first half free-kick that goalkeeper Dave Watson could not hold, leaving Steve Bould the simple task of smacking the ball home from six meters.
And as if to prove he could do it with his left foot as well, Bergkamp waited just four minutes to claim his sixth goal of the season from 20 meters with a cracking shot.
That effectively put the result beyond doubt, although Martin Keown emphasized Arsenal's superiority when he headed home 14 minutes from time.
Bolton, last season's beaten finalist, did most of the attacking but was unable to find the net as it was held to a goalless draw by first division Leicester.
The two sides, who swapped positions between the Premiership and Division One at the end of last season, put on an entertaining show but failed to produce a winning punch.
(For other results, see Scorecard.)
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The Spanish Football Federation announced on Tuesday that it has banned Barcelona coach Johan Cruyff for five matches and fined 500,000 pesetas ($4,000) for insulting a referee.
Cruyff jumped up from the dug-out early in Sunday's game between Barcelona and Valencia, after a tackle on Barcelona's Albert Celades, walked onto the Nou Camp pitch and argued with referee Manuel Diaz Vega, who showed him the red card. Cruyff was forced to watch the rest of Barcelona 's 1-0 win from the stands.
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