Ronald de Boer's late header proved enough to sink the plucky challenge of Ayr as holders Rangers progressed into the fifth round of the Scottish Cup.
With championship rivals Celtic having enjoyed UEFA Cup success in midweek to set up the prospect of fixture congestion, Rangers were 11 minutes away from adding an unwanted replay to their own busy calendar.
But de Boer's intervention turned out to be the significant one and the Ibrox giants marched on.
Ayr had given them a scare however, not least when teenage substitute Stewart Kean fluffed an excellent equaliser chance following confusion in the Rangers defence.
Dundee recorded their first Dens Park win over Aberdeen in seven years to book their place in the fifth round with a 2-0 win.
A superb first-half display from Dundee's trio of strikers blew away the Dons and despite missing a host of chances throughout the 90 minutes, the Dark Blues never looked in danger of recording anything but a win.
Top scorer Steve Lovell scored his 10th goal of the season after 22 minutes after taking advantage of some hesitant Dons defending.
Spanish winger Nacho Novo capped a fine performance by adding the second with four minutes of the first half remaining to compound yet another miserable afternoon for the Dons.
Dunfermline and Hibernian will need an Easter Road replay after a 1-1 draw.
A first-half strike from Ian Murray sent the Edinburgh side into the lead but
Barry Nicholson's excellent volleyed equaliser means the sides will have to try
again.
The Pars always came close to a winner in a pulsating second half but the
visitors' defence held firm in the frantic closing stages.
Motherwell striker James McFadden made a sensational return from suspension with two well taken goals which eased the Fir Park side past Clyde and into the quarter finals.
The Scotland international, back in the Fir Park side after a four-game ban, opened the scoring just before the break with a cool finish and a virtuoso goal in the second half killed off the spirited First Division side who fought hard but ran out of steam.
First Division Inverness overcame an early setback to cruise past Hamilton Academical 6-1.
Martin Bonnar slotted home a Gareth Armstrong cross in the second minute for the Accies.
But doubles from Dennis Wyness and Barry Robson and single strikes by Paul Ritchie and Stuart McCaffrey ensured a 6-1 victory for the Division One team.
Ian Harty struck twice to give Stranraer a 2-0 win over Morton and book a place in the quarter-finals for the first time in their history.
The Blues had to wait for 32 minutes before breaking the deadlock when Harty was first to react in a goalmouth scramble when a corner was headed down to him.
Then Third Division promotion hopefuls Morton gifted Harty his second when John Maisano needlessly handled in the area for the Stranraer forward to strike from the spot in the 52nd minute.
Goals from Owen Coyle and Collin Samuel ensured Falkirk's safe passage into
the quarter-finals at the expense of neighbours Alloa at Recreation
Park.
The Wasps had kept the scoreline goalless at half-time despite protests
against Lee Miller's disallowed 25th minute header.
But veteran Coyle settled the First Division pacesetters' nerves with a cool
finish seven minutes after the break.
Then, 13 minutes later, Samuel secured the win and a place in the last eight
for the Bairns.