Robbie Keane's second-half hat-trick took Celtic past Kilmarnock in their Scottish Cup quarter-final clash at Rugby Park.
The home side had the best of the first period with striker Allan Russell clipping the bar with a shot.
However, the tide turned in the 63rd minute when Keane opened the scoring from Edson Braafheid's long ball and two goals within a minute secured the visitors a place in Monday's semi-final draw.
Like last week's win at Falkirk, where Keane helped himself to a brace, the Republic of Ireland international showed why he is worth his 65,000 pounds per week wages with his eighth goal in eight games since arriving from Tottenham in January.
Raith Rovers earned a place in the last four with a hard-fought 2-1 win over below-par Dundee.
John McGlynn's side made an explosive start and opened the scoring after only three minutes when Stephen Simmons volleyed home from just inside the area.
Raith then doubled its lead in the 10th minute when Laurie Ellis powerfully headed in an Allan Walker free-kick.
Dundee gave itself a glimmer of hope when Craig Forsyth headed home after 73 minutes but despite a late rally the hosts could not find a second that would have forced a replay.
First Division side Ross County twice came from behind to earn a deserved replay against Hibernian.
The home side's hoodoo in a competition they have not won since 1902 could continue after Michael Gardyne's 80th-minute equaliser gave the Staggies another bite at the cherry at Victoria Park on Tuesday week.
Hibs could not have wished for a better start as Colin Nish gave them the lead in the seventh minute, but Ian Murray's own goal nine minutes later gave the Highlanders hope.
And, despite going in at half-time 2-1 behind after Derek Riordan's 19th-minute strike, County were more than worthy of Gardyne's volleyed equaliser after a magnificent second-half showing.
Meanwhile, in Premier League action, Flavio Paixao's injury-time winner saw Hamilton leapfrog St Mirren into 10th place with a 1-0 win at home.
Motherwell furthered its quest for a European place after a whirlwind start at Fir Park helped it to a 3-1 win and former Falkirk players Liam Craig and Kenny Deuchar came back to haunt their old club as St Johnstone claimed a precious comeback 2-1 victory at Westfield.
FA Cup results:
Dundee 1 (Forsyth 73)
Raith Rovers 2 (Simmons 3, Ellis 10)
Hibernian 2 (Nish 7, Riordan 19)
Ross County 2 (Murray 16og, Gardyne 79)
Kilmarnock 0
Celtic 3 (Keane 64, 81, 82)
Premier League results:
Falkirk 1 (Twaddle 27)
St Johnstone 2 (Craig 45p, Deuchar 84)
Hamilton 1 (Paixao 90)
St Mirren 0
Motherwell 3 (Reynolds 2, Sutton 13, O'Brien 68)
Hearts 1 (Templeton 69)