Celtic bounce back to join Rangers in League Cup semi-finals

Leigh Griffiths scored the only goal for Celtic against St Johnstone to ease the pressure on Brendan Rodgers. (AFP/ANDY BUCHANAN)

Steven Gerrard's Rangers also cruised into the last four with a 4-0 rout of second division Ayr United, while Premiership leaders Hearts came from behind to beat Motherwell 4-2.

Celtic will face Hearts in the semi-finals, while Rangers take on Aberdeen on Oct 28.

Leigh Griffiths grabbed the only goal for the holders in Perth, who had defender Dedryck Boyata sent-off in stoppage time, to maintain manager Brendan Rodgers' perfect record in domestic Cup competitions as Celtic boss.

"Psychologically, it's a good win for us," said Rodgers, who has won all six domestic trophies on offer in his first two seasons in charge.

"We've enjoyed the last couple of years at Hampden and let's hope we enjoy it this year as well."

Rodgers has come in for criticism in recent days after Celtic made their worst league start in 20 years with a 2-1 defeat at Kilmarnock on Sunday.

The former Liverpool manager revealed before kick-off he had turned down the opportunity to move to an unnamed Chinese club in the summer to concentrate on his job with the Scottish champions.

But Rodgers again had to watch his side labour again before Griffiths's strike seven minutes from time despite dominating possession.

The Scotland striker swept home the rebound after James Forrest's header was blocked and ran off to celebrate with his manager on the touchline in a sign of support.

Gerrard is experiencing no such strife at Ibrox as Rangers made have now racked up 13 goals in three home wins in 10 days.

Defender Nikola Katic headed home the opener from a corner before Glenn Middleton got the first of his double on the night.

The in-form Alfredo Morelos will be banned for the semi-finals after being booked, but grabbed his seventh goal of the season before Middleton rounded off the scoring.

The tie of the night was at Tynecastle where Hearts struck twice in the final two minutes through Olly Lee and Steven Naismith to see off Motherwell.

Curtis Main's early penalty for the visitors was cancelled out by Steven MacLean.

Peter Haring put Hearts in front but Ryan Bowman's powerful effort looked to have earned Motherwell extra-time before Lee and Naismith struck to continue a fine start to the season for Craig Levein's men, who lead the league by five points from Rangers.

"I thought it was a fantastic game of football," said Levein. "This group of players have got a spirit, a dig and a fight about them. Tynecastle brings out the best in them.

"It'll be a tough match (against Celtic) but the boys are in a good place just now and hopefully we'll be in the same sort of place come the semi-final."

Aberdeen complete the semi-final lineup after they edged out Hibs on penalties on Tuesday after a 0-0 draw at Easter Road.