Celtic avoided a repeat of their giant-killing at the hands of Clyde 14 years ago as a much-changed team eased to a 3-0 win at Broadwood on Sunday.
Hoops manager Neil Lennon was part of the side that lost to Clyde on Roy Keane’s Celtic debut in 2006 and his team selection offered the third-tier part-timers hope as he rested top scorer Odsonne Edouard among six changes.
Despite the change in personnel and a strong swirling wind, the holders were always in command after Olivier Ntcham fired home just 16 minutes in.
Celtic captain Scott Brown stabbed in a second five minutes before the interval and substitute Vakoun Bayo added a third in the final minute.
“We had a strong enough team out to make sure we didn’t want any cup upset or scare,” said Lennon.
“We played quite well in the conditions because they were very tough.”
Celtic have now won 33 consecutive domestic cup ties and will be confident of reaching the semi-finals again after being drawn away to St Johnstone in the last eight.
Earlier, Hibs eased into the quarter-finals with a 4-1 win at fifth-tier BSC Glasgow thanks to Marc McNulty’s hat-trick.
The Edinburgh side were the last team other than Celtic to win the Scottish Cup and will face Inverness Caledonian Thistle at home in the next round.
Rangers face a quarter-final trip to Hearts, where they have failed to win in two trips this season, and St Mirren or Motherwell will face Kilmarnock or Aberdeen with replays needed to find a winner from their ties on Saturday.