Steven Gerrard's side took the lead right at the end of the first half through Swedish defender Filip Helander.
Colombian striker Alfredo Morelos added the second goal just after the interval and Morelos wrapped things up with the third in 62 minutes.
It was the first meeting of the teams in this competition since the 2007/08 semi-final and was watched by a crowd of 49,310 at Hampden.
Rangers now face Celtic – who beat Hibernian 5-2 on Saturday – in the final next month.
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