Scott Brown found the target for the third game in a row as Celtic overcame a battling Inverness Caledonian Thistle 2-0 to reach the quarter finals of the Scottish Cup, while Motherwell crushed Morton and Hibernian edged out Kilmarnock.
Georgios Samaras handed Celtic a first-half lead and they had to withstand some pressure from Caley before Brown converted from the spot on 67 minutes to seal their passage.
Both sides took time to come to terms with the windy conditions but the pendulum swung the visitors' way when Greece striker Samaras fired high past Jonny Tuffey in the 33rd minute to give them the interval lead.
In the 67th minute, after Caley defender David Proctor had conceded a penalty for a foul on Gary Hooper, Celtic skipper Brown slotted in the spot-kick to take the holders into Monday's draw at Hampden Park.
The result extended the Hoops' domestic winning run to 15 games and, being one point clear of Rangers at the top of the SPL and in the final of the Scottish Communities League Cup final, kept them on course for the domestic treble.
Motherwell booked their place in the last eight with an emphatic 6-0 victory over Morton at Fir Park.
The home stunned their Scottish First Division opponents as they raced into a 5-0 half-time advantage. Tom Hateley netted directly from a corner before Jamie Murphy, Shaun Hutchinson, Henrik Ojamaa and Nicky Law all netted for the hosts as the tie was all but decided before the interval.
Murphy then blasted home his second midway through the second half to add to Morton's woes and complete a one-sided scoreline.
A first-half Eoin Doyle strike was enough to earn a resolute Hibernian side a 1-0 win over Kilmarnock at Easter Road.
Aberdeen came from behind to earn a replay against Queen of the South.
Scott McLaughlin netted against the run of play after 54 minutes to give the Doonhamers hope of pulling off a shock against their top flight rivals, who have fallen victims to a number of cup upsets in recent seasons. However Scott Vernon scrambled the ball home after 67 minutes following a long Kari Arnason throw-in to keep alive the Dons' hopes of reaching the quarter-finals.
Ross County captain Richard Brittain missed a last-minute penalty as the First Division side had to settle for a replay against St Mirren.
Brittain had put his side ahead from the spot five minutes before half-time, only for the effort to be cancelled out within three minutes by a headed goal from St Mirren striker Steven Thompson.
Brittain had a golden opportunity to score a stoppage-time winner after Mark Corcoran was brought down by Lee Mair, but this time he sent his penalty sailing well over the bar.