Celtic took another massive step towards their ambition of a domestic treble with a victory over St Mirren in the Scottish Cup at Celtic Park on Sunday.

Surviving an early scare, in the end the Bhoys' quality shone through with an impressive second half showing that sent the Buddies packing despite a spirited first half performance.

That performance saw the Paisley side go into the break 1-0 up thanks to a Harry Davis goal from a John Sutton knock down. At that point in the afternoon things were looking pretty dire for Brendan Rodgers' team and things could've gotten worse early in the second half when a Moussa Dembele mis-kick ricocheted off his own bar.

That Dembele incident seemed to spark the Hoops into life though and, inspired by Rodgers' substitutions, the team pushed on to eventually blow Jack Ross' side away with goals from Mikael Lustig, Scott Sinclair, Dembele and Leigh Griffiths.

The win puts them into the semi-finals of the Scottish Cup where they'll face Rangers in a massive clash at Hampden.

Here are FIVE lessons we learned from Celtic's quarter-final win...

Leigh Griffiths is still absolutely vital

Leigh Griffiths hasn't had the best of starts to 2017 having not started any games and only featuring from the bench twice prior to Sunday's encounter. However he'll have done his chances of more regular appearances the world of good after his dynamic display in the second half on Sunday.

He came off the bench with the Hoops 1-0 down and won the free-kick that resulted in Mikael Lustig opening the scoring before providing the assist for Scott Sinclair to curl home and put Celtic ahead. Later getting on the scoresheet himself, it's clear he was the catalyst for the win and keeping the Bhoys' treble dreams alive.

The emergence of Moussa Dembele has meant Leigh Griffiths is no longer the main man around Celtic Park but Sunday's showing showed that he is far from done and dusted in a green and white shirt.

Patrick Roberts should play ahead of Gary Mackay-Steven

Gary Mackay-Steven had a woeful first half at Celtic Park, seemingly unable to provide any sort of chance for Celtic despite finding a tonne of space on the right hand flank. The Hoops looked a bit toothless in all honesty and it wasn't until Patrick Roberts came on at half-time that it began to change.

Roberts may be on his way back to Manchester at the end of the season and that may be influencing Rodgers' hesitance to start him at the expense of permanent members of the squad but it's clear that if James Forrest is out then Roberts should be starting.

Going into next week's derby at Celtic Park with Mackay-Steven on the wing would be a mistake and Rodgers must consider unleashing the young English winger from the start, even if it means leaving out one of the club's assets in the cold.

Moussa Dembele can't stop scoring

Moussa Dembele has now scored an incredible 12 goals in his last 6 matches and no matter the occasion seemingly is always able to find the net. He really kicked his game up a gear in the second half after a fairly poor first 45 minutes by his standards and got onto the end of Scott Sinclair's low cross after some find counter-attacking play.

He's now on 32 goals for the season and is rapidly closing in on Leigh Griffiths' 40 goal total of last season. Can he reach that milestone? We wouldn't like to bet against it.

There is a game plan to defeating Celtic

St Mirren manager Jack Ross proved again he is one of the brightest managerial prospects in Scotland after inspiring his struggling Buddies side to a hell of a performance at Celtic Park, at least for the first hour anyway.

Brendan Rodgers went so far to say that St Mirren were the toughest Scottish side Celtic have played all season, even compared to Premiership sides, which is high praise indeed for the performance of Ross' men.

The St Mirren manager proved in the first half that Celtic are not unbeatable and that there is a gameplan to defeating them. The key to it all appeared to be shutting down the left hand side and squeezing the space between Kieran Tierney and Scott Sinclair. It took them out of the game and meant that Celtic's only outlet was Gary Mackay-Steven on the right hand side who squandered opportunity after opportunity.

It was a very interesting tactical battle and while Celtic of course eventually came through unscathed, was perhaps a window into a potential future defeat for the Bhoys.

The treble is hard to argue against

Celtic are well on their way to a domestic treble of trophies, a feat that would only be achieved for the fourth time in their history if it happened. It's hard to argue against it given not just the form of the Hoops but their resiliency too. Even when they go behind Rodgers finds a way to change the team, players find a way to win individual battles and collectively they find a way to win.

There are big tests to come at Hampden of course, a place that has sometimes been unkind to the Hoops over the last decade, but this Rodgers side seem to have a steely quality that just cannot be denied.

Can anyone stop them?