Aiden McGeady returned from his club ban to help Celtic come from behind and earn a Scottish Cup win over Dundee.
Celtic goalkeeper Artur Boruc's fresh-air swipe in the 14th minute allowed Colin McMenamin to put the First Division side in front but Scott Brown levelled after a mis-hit effort from Scott McDonald rebounded into his path.
McGeady, back for the first time since his dressing-room row with the Celtic manager Gordon Strachan, curled in the winner on the stroke of half-time.
Elsewhere in the Scottish Cup, Ayr United and Kilmarnock fought out a thrilling draw in a blood-and-thunder tie at Somerset Park. The visitors took the lead after nine minutes when Manuel Pascali tapped home a cross from David Fernandez. However, the Division Two side levelled five minutes later when Dean Keenan headed past goalkeeper Damien Rascle.
Kilmarnock's Craig Bryson made it 2-1 from Willie Gibson's centre and Allan Russell missed a penalty chance to make it 3-1 before Alex Williams' volley saved Ayr.
Aberdeen gained a hard-fought victory against Alloa Athletic. The visitors took a ninth-minute lead when Chris Maguire's shot deflected off team-mate Lee Miller and beyond the Alloa goalkeeper Raymond Jellema. But Alloa levelled from the penalty spot, Andy Scott converting three minutes before half-time. Sone Aluko got Aberdeen's winner in the 57th minute when he got in behind the Wasps' defence and lobbed Jellema.
Falkirk reached the fifth round after overcoming a plucky Queen of the South 4-2. Scott Arfield's 37th-minute penalty put Falkirk in front from the penalty spot but Queens equalised before half-time with a deflected Barry Wilson shot.
Bob Harris' superb free-kick put the visitors in front early in the second half but Arfield quickly equalised. Graham Barrett put the Bairns back in front on 68 minutes and thestriker added a fourth late on.
Filipe Morais marked an impressive Inverness debut with two goals in the 3-0 win over Partick Thistle. The Portuguese midfielder let fly with a long-range effort on 28 minutes and it took a huge deflection on its way past the goalkeeper Jonathan Tuffy. Early in the second half Iain Vigurs smashed home a sweet strike from just inside the penalty area and Morais grabbed his second on 56 minutes when he scuttled through to poke a shot beyond Tuffy.
Spartans' adventure ended in a 2-1 defeat at Airdrie, Hamilton won 1-0 at Ross County, Dunfermline beat Clyde 2-0 and East Fife won 1-0 at Stenhousemuir.