Celtic will play Dundee United in the final of the Scottish League Cup, presented by QTS, on Sunday March 15.
Ronny Deila's side defeated Rangers 2-0 at Hampden on Sunday afternoon to set up a meeting with Jackie McNamara's men, who beat Aberdeen 2-1 on Saturday.
Leigh Griffiths headed Celtic in front from a Stefan Johansen cross after 10 minutes and Kris Commons thundered the second past Steve Simonsen from outside the box on the half-hour.
There were few clear-cut chances during the second half of the first Old Firm game since April 2012, with Rangers unable to seriously test Craig Gordon.
Celtic will now hope to win their first League Cup since 2011 when they play a Dundee United team who have lifted the trophy twice – in 1979/80 and 1980/81.
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