Celtic cruise through, Rangers edge past Livi in League Cup
Hearts beat Aberdeen on penalties and Hibs defeated Kilmarnock after a shootout.
Celtic 5-0 Partick Thistle
Celtic boss Neil Lennon made eight changes to his side but saw them cruise into the last four as they continued their defence of the trophy.
Vakoun Issouf Bayo opened the scoring with a header from a Jonny Hayes free-kick, giving Thistle an uphill battle in front of new manager Ian McCall.
There was no further scoring in the first half but just seconds after the restart Celtic doubled their lead with Bayo setting up Tom Rogic ,who slotted the ball past Scott Fox.
Olivier Ntcham then scored a quick double, slamming in a long-range shot for his first and then finishing a quick counter to make it 4-0.
Scott Sinclair came off the bench and wrapped up the scoring with a fifth and Celtic took their place in the semi-final draw.
Hearts 2-2 Aberdeen (aet. Hearts 3-0 on penalties)
Hearts hit the bar in the first minute and were on top at Tynecastle only to go behind after 12 minutes.
Christophe Berra brought down Ryan Hedges in the box and Sam Cosgrove stepped up to score the resultant penalty.
Hearts hit back almost immediately when Steven McLean scored but hopes of continuing their momentum evaporated when Loic Damour brought down James Wilson to concede another spot kick. Cosgrove took responsibility again and restored his side's lead.
The hosts kept pushing and as the clock ticked down on the second half it looked like their efforts would be in vain but injury time brought a last chance when Jake Mulraney put in a cross and Craig Halkett headed into the net to force extra time.
There was no further scoring and penalties were needed to decide who would go to Hampden.
Cosgrove took Aberdeen's first and put it over the bar, handing Hearts the advantage. Niall McGinn and Bruce Anderson also missed with Hearts scoring all three to take their place in the semi-finals.
Kilmarnock 0-0 Hibs (aet. Hibs won 5-4 on penalties)
Hibs were looking to bounce back after their derby defeat and Paul Heckingbottom brought summer signing Christian Doidge into his side looking for the goals to progress to the semis.
Killie were hoping for a repeat of their recent 2-0 league win over the Edinburgh side to keep their run going but chances were few and far between in a flat encounter at Rugby Park.
Neither side could find a goal in regulation time and the stalemate continued through the added half hour.
Hibs were reduced to ten men in the final minutes when Ryan Porteous was shown a straight red card for a late tackle.
Stephen O'Donnell had a late chance to settle things but put his header wide and penalties were needed to settle the tie. Hibs' Oli Shaw and Kilmarnock's O'Donnell both failed to score before Niko Hamalainen missed the last for Killie, sending Heckingbottom's side to the national stadium.
Livingston 0-1 Rangers
Rangers booked their place at Hampden thanks to a goal from Glen Kamara.
The visitors were ahead after just four minutes. Nicky Devlin's clearance landed at the feet of Kamara and the midfielder struck a powerful shot that deflected off Devlin's knee and past Matija Sarkic.
Livingston pushed to get back into the game but couldn't the goal they need and Rangers were unable to find the second that would allow them a degree of comfort.
Steven Gerrard's side saw out the remainder are are now just one match away from the first final of the season.
League Cup semi-final draw
Rangers will face Hearts in the semi-finals with holders Celtic drawn to face Hibs.
Ties will take place on the weekend of November 2.