Midfielder Darren Ramsay netted the only goal of the game in Paisley to give the Light Blues victory and set up a meeting with Hearts who beat Kilmarnock 3-0 on Saturday.
The Saints, who handed a start to first team keeper Chris Dilo, had defender Barry Caddihy sent off for a foul on Ramsay and Gers boss Gordon Durie hailed his side for digging in to see off the battling Buddies.
He said: "We're delighted to be in the final. I think we deserved to win the game, especially after they had a man sent off. They really sat in from that point.
"We've been there before and I've done that myself. They had two banks of four and just one boy up front and they made it difficult to break them down.
"It's hard to play against a team like that but we fully merited our victory. We bossed the game and I'm really happy for the boys.
"We've played Hearts once this season and drew 1-1 at Murray Park. They deserved their victory in the other semi-final by all accounts and it should be a good game."
Victory at St Mirren Park was the third time Rangers have beaten their near-neighbours this season having won both Under-20 league fixtures against a Buddies side struggling in the standings.
There was to be no upset as the Saints fell short once again and Durie was pleased to see his kids finally get over the line.
"Their goalie had an excellent game today and it was going to take a worldie to beat him but Darren's capable of that," he told rangers.co.uk
"We were actually going to take him off a couple of minutes beforehand because he could hardly move.
"It was a wise decision by the staff to keep him on and it was a great goal for us so now we're looking forward to the final."