Scottish review:A Steven Whittaker double in extra-time saw Rangers book their place in the fifth round of the Active Nation Scottish Cup after beating Hamilton 2-0, while Niall McGinn struck Celtic's winner against Morton in their fourth round tie.
McGinn's left-footed strike after 35 minutes gave Celtic victory at Cappielow.
The Clydesdale Bank Premier League side had not seriously troubled Ton goalkeeper Colin Stewart before striker Marc-Antoine Fortune cut the ball back for the former Derry City player who drove past Stewart from 12 yards.
From then on the visitors looked comfortable as Morton never really threatened a shock.
Celtic will now go away to Irn-Bru Second Division side Stenhousemuir in the next round if Dunfermline, who were thrown out of the competition by the Scottish Football Association for breaking various rules in their win against the Warriors, do not win their appeal.
Rangers were meeting Accies for the third time in 10 days, having drawn 3-3 in the Cup at the first time of asking before winning narrowly in the league at the weekend.
Accies once again frustrated the holders and forced the replay to extra-time, but two goals in four minutes from Whittaker ensured Rangers progressed to a meeting with St Mirren in the next round.
Rangers immediately set about trying to put Hamilton under pressure when Kenny Miller raced onto a lovely ball from Danny Wilson and stung the palms of Tomas Cerny with a blistering shot early on.
The home side continued to press and Miller went to ground in the box claiming he had been fouled by Simon Mensing, but no penalty award was forthcoming from referee Charlie Richmond.
Rangers were always creating the best of the chances and a cross from the right from Whittaker was nodded on by Miller for Steven Davis, but he bulleted his own header wide.
Only the woodwork prevented Miller from finding the back of the net when he ran on to a Papac pass and saw his shot at full stretch crash off the crossbar.
A combination of poor finishing and staunch defending ensured the tie finished goalless after 90 minutes and went into extra-time.
Accies could have snatched a goal in the opening minute when Mickael Antoine-Curier whipped a teasing ball to the feet of substitute Kyle Wilkie, but his poor effort rippled the side netting.
The breakthrough finally came after 95 minutes when Miller squeezed between two defenders and flighted the ball over Cerny - who got a touch on it - and Whittaker was waiting to bundle home from almost on the goal-line.
Whittaker then grabbed his second of the night just four minutes later, this time collecting a Fleck pass before lofting over the Accies goalkeeper and into the top corner.