Adam Rooney scored a second-half hat-trick as Aberdeen began their defence of the Scottish League Cup with a 4-0 win over Livingston at Pittodrie on Tuesday night.
Ash Taylor broke the deadlock early on and Rooney doubled the advantage on the hour mark before adding two more goals.
Brian Graham scored the only goal early in the second half as St Johnstone edged out Kilmarnock 1-0 at Rugby Park. Killie had Alexei Eremenko sent off with 20 minutes left.
Rangers came from behind to win 3-1 at Falkirk, who went ahead in five minutes through Rory Loy. The visitors equalised soon after with an Owain Tudur Jones own goal. Dean Shiels scored the second in 65 minutes before Ian Black sealed the victory in stoppage time.
Hibernian claimed a 2-0 win over Ross County at the Global Energy Stadium thanks to a first-half double from Dominique Malonga. Alan Stubbs's side had Dylan McGeouch sent off in the closing stages but County couldn't take advantage.
Partick Thistle gained revenge for Friday's defeat in the Premiership by beating St Mirren 1-0 at Firhill. The only goal came in the first period of extra time from Nathan Eccleston.
There are three more third-round ties on Wednesday - Celtic v Hearts, live on BBC Scotland at 7.15pm, Dundee United v Dundee and Hamilton Accies v Motherwell.
The quarter-final draw will be made at Tannadice after tomorrow's matches and will be broadcast live on BBC Radio Scotland's Sportsound programme (810 MW).
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