Rangers cruised into the semi-finals of the Scottish Cup with a 3-0 win over Dundee at the Kilmac Stadium. The defender Connor Goldson drove them ahead in the ninth minute before the captain, James Tavernier, scored a penalty after 24 minutes and the Premiership’s bottom team had no answer. Giovanni van Bronckhorst’s side controlled the rest of the game, with the substitute Fashion Sakala adding a third with three minutes remaining. It was the end of a good week for Rangers, who beat Aberdeen 1-0 in the Premiership last Saturday before a 3-0 victory over Red Star Belgrade in the first leg of their Europa League last-16 tie at Ibrox on Thursday. They joined Hearts and Hibernian in the last four, and the winner of Monday night’s Dundee United versus Celtic tie at Tannadice will complete the lineup. Dundee will welcome Rangers on league duty next Sunday, when survival points are required. Van Bronckhorst shuffled his pack after his side’s European exertions. The midfielder Aaron Ramsey made only his second start since arriving on loan from Juventus in January while Jon McLaughlin, Filip Helander and James Sands also came in. Dundee showed three changes with Lee Ashcroft, Paul McGowan and Daniel Mullen returning. Rangers took their early lead after Calvin Bassey won a corner. Helander got his head to Tavernier’s delivery and although Ashcroft cleared the ball on to the crossbar it bounced back out to Goldson, who returned it into the net from 14 yards with a thumping shot. In the 14th minute Alfredo Morelos missed the target from 12 yards before Harrison Sharp made a fine save from Ramsey’s drive moments later. Dundee did carve themselves a chance in the 20th minute with Niall McGinn’s free-kick into the packed penalty area but Ashcroft headed wide from six yards and they soon found themselves further behind. When the Dundee defender Ryan Sweeney’s block prevented Tavernier progressing any further, the referee, Steven McLean, pointed to the spot and Tavernier, who scored with a penalty against Red Star, drove the ball high past Sharp. Goldson blocked a shot from Max Anderson but that only inspired the visitors to step up the pressure. Their third goal came when Sakala, played in by his fellow substitute Alex Lowry, rifled the ball low past Sharp to put a truer reflection of the contest on the scoreline.