Giorgos Giakoumakis scored a second-half double as Celtic booked their place in the Scottish Cup semi-finals with a straightforward 3-0 win over Dundee United at Tannadice.
The visitors, who made it 30 domestic matches in a row unbeaten, were comfortable for most of the evening following Callum McGregor 's early opener, although they were aided significantly by a terrible blunder from United goalkeeper Benjamin Siegrist for their second goal.
The result means the last four of Scotland's oldest knockout tournament is made up of the two big clubs from Glasgow and Edinburgh for the first time in its history.
United manager Tam Courts made two changes to the side that drew with Hearts in their previous match as Scott McMann and Kevin McDonald dropped out to make way for Kieron Freeman and Dylan Levitt.
Ange Postecoglou made four alterations to the Celtic side that won 3-1 at Livingston in the cinch Premiership last time out. Anthony Ralston, Tom Rogic, Nir Bitton and Jota dropped out to be replaced by Josip Juranovic, Matt O'Riley, Reo Hatate and Giakoumakis.
The visitors threatened after three minutes when Daizen Maeda's speculative effort from wide on the left almost dropped in at the far post.
Celtic made the breakthrough in the 12th minute as McGregor's angled strike from just outside the box took a deflection off Nicky Clark on its way into the net. O'Riley had taken a short corner to James Forrest, who then teed up the Hoops captain.
United were forced into a change in the 28th minute when Ian Harkes went off injured and was replaced by McDonald.
Celtic looked fortunate to keep 11 men on the pitch in the 31st minute when Hatate escaped with a booking for a rash challenge on Freeman.
The visitors thought they had doubled their lead five minutes later as Maeda turned the ball in from close range, but the officials halted the celebrations as Giakoumakis had kicked the ball off his own hand in the build-up when attempting to control Juranovic's cross from the right.
McGregor then fired just wide from the edge of the box before Giakoumakis hooked an effort past a post from a Forrest cross.
Celtic made their first change of the night at the start of the second half as Rogic replaced Hatate.
The Parkhead side stretched their advantage in the 58th minute when United keeper Siegrist made a howler as he dropped a harmless Maeda cross at the feet of Giakoumakis, who had the simple task of knocking the loose ball over the line.
The Greek striker then tapped in the Hoops' third in the 88th minute after being set up by substitute Karamoko Dembele.
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