Stand-in centre-forward Daizen Maeda netted a hat-trick as a much-changed Celtic eased past Raith Rovers in the Scottish Cup.
Hyun-Jun Yang produced a goal and two assists and Luke McCowan was also on target as Brendan Rodgers' clinical side progressed to the quarter-finals with a 5-0 home win.
Maeda was the star of the show to take his tally to six goals inside a week as he again showed he could help Celtic cope with the exit of Kyogo Furuhashi and their failure to bring in a replacement striker ahead of the transfer deadline.
However, an injury to Paulo Bernardo meant the tie was not a complete success for the holders as they warmed up for Wednesday's Champions League knockout phase play-off against Bayern Munich.
The Portuguese midfielder walked off before the half-hour mark after suffering a lower-leg problem.
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Queen's Park midfielder Seb Drozd wrote himself into Scottish Cup history by sinking Rangers with a stunning winner at Ibrox where Gers skipper James Tavernier had a last-gasp penalty saved by Calum Ferrie.
The famous old competition was Philippe Clement's side's last realistic chance for a domestic trophy this season as the Gers sit 13 points behind Premiership leaders Celtic, who beat them in the Premier Sports Cup final in December. The Light Blues are through to the last 16 of the Europa League.
Callum Davidson's Championship side kept a below-par home side at bay in the fifth-round tie before scoring the only goal in the 69th minute through substitute Drozd, the Englishman who signed last October from Millwall.
The home side were dramatically awarded a penalty in the fifth minute of added time when William Tizzard fouled Cyriel Dessers but Tavernier saw his spot-kick saved by Ferrie.
One of the greatest shocks in Scottish football history will put Clement back under the spotlight and the boos rang round Ibrox after a defeat which had been unthinkable before the game.
Aberdeen took some relief from their wretched Scottish Premiership form as they overcame Dunfermline to progress to the quarter-finals.
The Dons were on top throughout and took a deserved lead on the stroke of half-time though Pape Habib Gueye, with Alexander Jensen netting a first Dons goal five minutes after the restart.
Kevin Nisbet made up for missing an earlier gilt-edged chance with a late tap-in to make it 3-0 as Jimmy Thelin's men claimed only their second win in 16 matches - both victories coming in the cup.
Livingston had ended the run of Cove Rangers with a 2-0 fifth-round win in West Lothian.
Rangers, the last surviving League One outfit, fell behind in the 25th minute when Ryan McGowan turned in a free-kick.
Any hopes of a comeback were ended after a late double from Livingston substitute Tete Yengi.
Dundee eased through to the quarter-finals of the Scottish Cup with a comfortable win over Airdrieonians at Dens Park.
The hosts completely dominated the first half, netting four times thanks to goals from Clark Robertson, Seun Adewumi and a Lyall Cameron double.
After the break, Airdrie managed to shut up shop but the damage had already been done for the Championship strugglers.
Dundee will also take comfort from the win and the clean sheet after being hit for six in successive league games against Hearts and Celtic.
Adama Sidibeh ended his six-month goal drought to send St Johnstone through to the last eight with a 1-0 win over second-tier Hamilton.
A hugely frustrating afternoon for the Scottish Premiership's bottom side looked like continuing into extra-time against Championship strugglers Hamilton.
But Makenzie Kirk, who missed three excellent chances, made way for Sidibeh in the 84th minute and three minutes later the Gambian striker netted for the first time since an away win over Kilmarnock in August.
This nervy 1-0 victory for Simo Valakari's side marks the first time since 2018-19 that Saints have won four games in a row.
The draw for the quarter-finals will take place after St Mirren vs Hearts on Monday night.