Celtic successfully began their defence of the CIS Insurance Cup with a 2-0 win over St Mirren, while St Johnstone, Kilmarnock and Falkirk also progressed.
Gordon Strachan's side, whose victory over Dunfermline secured the cup last March, were pushed hard by The Saints at Celtic Park
There were no goals in the first half as St Mirren hunted a famous upset, although the visitors were indebted to goalkeeper Tony Bullock.
Bullock twice denied Craig Beattie with superb saves, while the crossbar also came to his rescue.
St Mirren continued to battle hard after the break, before Beattie took his revenge on Bullock in the 76th minute, smashing the ball into the net after being set on his way by Stephen Pearson.
Maciej Zurawski grabbed a late second three minutes from time.
In the other all-SPL clash, Falkirk edged past Inverness Caledonian Thistle 1-0.
Both sides have struggled so far this term, and the Highlanders' misery continued as Anthony Stokes won the game for Falkirk on the hour mark.
St Johnstone kept up their good form with a 3-0 victory over Dundee United.
Jason Scotland scored his eighth goal of the season five minutes before half time, before Steven Milne (53) and Simon Mensing (80) secured St Johnstone's place in the next round.
In the night's final game, Kilmarnock saw off a stubborn Livingston side 2-1 after extra time.
Gary Wales opened the scoring for Killie after 57 minutes, only for Steven Craig to level matters from the penalty spot (72).
The sides could not be separated after 90 minutes and penalties looked likely, before Frasier Wright scored in the 115th minute to knock out Livingston.
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