A second-half header from Lorenzo Amoruso was enough to beat Dundee and enable Rangers to complete their seventh Scottish treble by lifting the Tennent’s Scottish Cup.
The Italian, who is subject of a bid from Blackburn, headed home a Neil McCann free-kick.
It was tough on Dundee, who had the better chances throughout the game but could not convert them.
Rangers boss Alex McLeish admitted his side had almost run out of gas as they completed a domestic treble in his first full season in charge.
It was a lacklustre game but McLeish did not criticise his team who had been through an exhausting 90 minutes in winning the league with a 6-1 defeat of Dunfermline last Sunday.
“We were walking on empty,” McLeish told Sky Sports 1.
“We needed to score because the extra-time would have killed us.
“It was a big high last week, you can see one or two players are struggling.
“But I’m proud of the players proud of my staff and pleased for the fans.”