It was not all plain sailing, however, with Barjonas getting the wrong side of King and the challenge giving referee Kevin Clancy a decision to make. He saw no infringement and Airdire did not have the benefit of VAR to make their case. King also escaped punishment for an untidy block on Strapp.
Strapp's shot was a warning and Henderson soon took Barjonas' slipped past and buried past Shamal George.
However, St Mirren gathered themselves and their quality shone through in extra time.
And Idowu told BBC Scotland before receiving his player of the match award: "It came to me and I just, thought, 'should I take a touch or just hit it?' It just sat perfectly for me so I just took the strike.
"We got the result so that's all that matters. We're still on a bit of a streak.
"When we were on the cup run at the start [of the season], it was almost like the impossible. Now, we know it's very possible so whatever the draw is, we go with the same attitude of, 'we've done it before, we know what it takes to get to that level', so we definitely are anticipating good things."