Gary Hooper helped himself to four goals as Celtic eased their way past Raith Rovers 4-1 at Parkhead to book their place into the quarter-finals of the Scottish Communities League Cup.
The Hoops striker opened the scoring in the 12th minute with a trademark poacher's goal before Raith skipper Allan Walker levelled in the 27th minute with a deflected shot from 20 yards.
However, Hooper minimised any chances of a cup upset when he restored Celtic's lead before the break before completing his scoring spree in the second half against the Irn-Bru First Division side who were valiant but out of their depth.
Lee Mair grabbed a last-gasp winner as St Mirren scraped past Hamilton 1-0 to reach the quarter-finals.
The meeting at St Mirren Park appeared to be heading for extra-time, with nothing to separate the two sides until Mair struck deep into injury-time to ensure the Buddies' name would be in the draw for the next round.
Johnny Russell sent Dundee United into the quarter-finals as the Tayside club's first goal in four games ended Queen of the South's unbeaten start to the season.
Russell converted Michael Gardyne's cross at the second attempt in the 28th minute as United edged a tight first half at Palmerston.
The Irn-Bru Second Division leaders had won 10 times, including cup triumphs against Hibernian and Rangers, and drawn once previously this season and they put United under sustained pressure after the break but could not finish their chances.
Hearts captain Marius Zaliukas went from villain to hero as the Tynecastle side progressed to the last eight with a 3-1 victory over Livingston.
The Lithuanian defender was responsible for the visitors' equaliser, slipping at the vital moment to allow Mark McNulty to scamper through on goal and make it 1-1 in the second half.
That cancelled out a first-half Danny Grainger goal, but Zaliukas made amends in determined fashion, bundling home two goals in the last 15 minutes to ensure there would be no cup shock in Edinburgh on Tuesday night.
Inverness scraped through to the quarter-finals with a tense 6-5 penalty shoot-out victory over Stenhousemuir.
There was little to separate the teams after a 1-1 stalemate in 90 minutes and there was no further goals in extra-time, then Ryan Esson produced a good stop from Darren Smith's penalty to end the Irn-Bru League Division Two side's hopes of an upset.
The visitors opened the scoring after 24 minutes when Billy McKay raced onto Richie Foran's through ball and lobbed the ball over Robbie Thomson.
Stenhousemuir were awarded a penalty five minutes before the break when David Raven chopped down Brown Ferguson and the striker got up to convert the resulting kick beyond Esson.
St Johnstone secured their place in the last eight after a 4-1 win over 10-man Queen's Park at McDiarmid Park.
A first-half double from new striker Steven MacLean followed by late goals from Murray Davidson and substitute Liam Craig sealed the third-round tie for Steve Lomas' side who survived a slight scare when midfielder Michael Keenan levelled for the plucky visitors on the half-hour mark.
Queen's Park were reduced to 10 men when full-back Andrew Robertson was shown a straight red card from referee Kevin Clancy for a late lunge on Gary Miller before Davidson and Craig both struck.