CELTIC had to come from behind to beat spirited second tier rivals St. Mirren 4-1 and book their place in the William Hill Scottish Cup semi-final.

Goals from Mikael Lustig, Scott Sinclair, Moussa Dembele and Leigh Griffiths kept alive their hopes of winning their fourth domestic treble.

But Brendan Rodger's side had trailed opponents who are five points adrift at the bottom of the Ladbrokes Championship by 1-0 at half-time.

They had conceded the opening goal to Harry Davis in the 13th minute and had struggled to get back on level terms against Jack Ross's team.

However, Rodgers replaced Gary Mackay-Steven with Patrick Roberts and Nir Bitton with Griffiths and his charges blew away their rivals in the second half.

Celtic started brightly with Stuart Armstrong, playing just behind lone striker Dembele once again in the continued absence of Tom Rogic, forcing a save from Billy O’Brien with a low shot in the third minute.

Mackay-Steven should have done far better after being released into the opposition box by Armstrong in the ninth minute. He failed to even get a shot away before being dispossessed.

The visitors took the lead after a well-worked move. John Sutton nodded a Cameron Smith cross from the left wing down to Davis who swept the ball past Craig Gordon from close .

It was the first goal Celtic had conceded at home since Marcus Haber had netted for Dundee in a Ladbrokes Premiership game on December 17 over two and a half months earlier.

They certainly responded well to falling behind. Brown went close after Mackay-Steven and Sinclair combined to tee their captain up with a shot from the edge of the area.

Brown supplied Dembele with a chance to level six minutes before half-time after cutting the ball back from the byline – but the striker hooked his attempt wide as well.

St. Mirren broke straight up the park and only a well-timed tackle from Celtic centre half Dedryck Boyata prevented their striker Sutton getting a shot away.

Roberts replaced Mackay-Steven, who had inadvertently been kicked in the head by Stelios Demetriou as he tried to win the ball in the first-half, at the start of the second 45 minutes.

But Ross’s side very nearly edged further in front in the 53rd minute after their opponents failed to clear a Stephen Mallan free-kick.

Dembele only succeeded in diverting the ball onto the underside of his own crossbar. It was a minor miracle that it stayed pout of his net.

Griffiths took over from Bitton a minute later and won the free-kick in the 59th minute which his side scored from after being fouled by Demetriou.

Roberts floated a high ball into the St. Mirren box and Lustig rose unchallenged and glanced it beyond O’Brien.

Less than 60 seconds later Rodgers’s side was in front after a stunning solo effort from Sinclair. The winger curled the ball past St. Mirren right back Gary Irvine and into the top right corner.

Sinclair also created Celtic’s third in 67th minute. He broke upfield from deep inside his own half, played a one-two with Roberts before squaring to Dembele.

The Frenchman side-footed the ball into an empty net to take his tally for the 2016/17 campaign to 32. Griffiths got in on the goals in the 77th minute when he lashed one in from fully 25 yards out.

Eboue Kouassi, the Ivorian midfielder who signed in a £2.8 million deal in January, made his first team Celtic debut when he came on for Armstrong.