Buddies assistant James Fowler and Bairns goalkeeping coach Derek Jackson squared up to each other in the technical area after the Saints man had been moaning about an offside decision.
And Falkirk’s Muirhead caught Stelios Demetriou with an elbow 13 minutes from time when the game had already gone for Peter Houston’s side.
Saints boss Jack Ross said: “I don’t think there was much in it, but you have to wait to see what reports are submitted.
“I like Don Robertson as a referee and at half-time he said he didn’t really see much of it. He had to go on his assistant’s decision.”
Peter Houston agreed when said: “James was having a go at the linesman and I said something to him and then my goalie coach got involved, but dugouts fall out all the time.”
It had all starred so well for Falkirk when they took the lead inside two minutes and dominated the first 20 minutes.
Craig Samson could only parry Rory Loy’s shot and Nathan Austin’s rebound header was over the line before Samson clawed it away.
It was Demetriou who sparked he comeback when he took a pass from Cammy Smith in 33 minutes and drove a left foot shot past Robbie Thomson.
Then Smith fired the Saints ahead two minutes into the second half when Thomson flapped at a Gavin Reilly cross and the former Aberdeen player fired into the unguarded net.
Reilly, pictured left, sealed it for Saints in 69 minutes when Smith cleverly played him in with a measured pass into the left side of the box and Reilly drove a left foot shot across Thomson into the right corner.
A miserable day got worse for Falkirk 13 minutes from time when Muirhead was sent packing for elbowing Demetriou.
Delighted Ross said: “We have a lot to be pleased about, particularly with the calibre of opposition and where they have been in recent seasons.
‘We finished last season so well and there is optimism around the club. It’s nice to keep the feeling going because there is a different vibe now.”
Conversely, Houston was critical of his team’s performance. He said: “We played as individuals, especially second half. We didn’t play as a team.
“St Mirren deserved to win but it’s a marathon this league and thankfully we have a game on Tuesday to try to rectify things.”