(CNN) -- St Mirren's 'reward' for their shock weekend Scottish Cup triumph against Celtic is a semifinal clash against the other Glasgow giants, Rangers.
The Paisley side were paired with the holders who hammered Hamilton 5-1 at Ibrox shortly before Sunday's draw that saw Falkirk face the winners of the replay between Aberdeen or First Division side Dunfermline
St Mirren are bidding to reach their first Scottish Cup final since 1987 when they beat Dundee United at Hampden Park.
Former captain and manager Tony Fitzpatrick, who was in the winning line-up 22 years ago, believes his old club will deserve to win the competition if they beat the other half of the Old Firm.
He told PA Sport: "In a cup competition you have to beat the best. But if I`m being honest, I would have loved St Mirren versus Rangers to be the final.
"But it`s an exciting draw and it will be a big occasion and after Saturday`s result against Celtic, St Mirren do have a chance. And let`s be honest, if they beat Rangers then they deserve to win the trophy."
Rangers assistant boss Ally McCoist, who now turns his attention to the Co-Operative Insurance Cup final against Celtic next Sunday, was pleased with the chance to make another final.
"It`s a great draw and I`m sure they will say the same," McCoist told BBC Scotland. "The most important thing is that we got there and it`s an opportunity to go back to the national stadium.
"St Mirren are there on merit and it was a wonderful performance yesterday, it really was."
Billy Mehmet's second-half penalty gave St Mirren a sensational quarterfinal win.
There were 55 minutes on the clock when Celtic captain Stephen McManus brought down Craig Dargo inside the box and striker Mehmet sent goalkeeper Artur Boruc the wrong way from the spot.
Celtic threw everything forward, but home goalkeeper Chris Smith made amends for his nightmare last week with a fine save at the end, from a Jan Vennegoor of Hesselink header, to prevent a replay.
Premier League bottom side Falkirk progressed after Carl Finnigan scored the only goal in a 1-0 win at 10-man Inverness.
The turning point came just after the half-hour mark when Lionel Djebi-Zadi was sent off for a professional foul on Finnigan in the penalty area. The striker took the spot-kick himself and smashed the ball past goalkeeper Ryan Esson.
Saturday's other match saw Aberdeen held to a 1-1 draw at Dunfermline. Nick Phinn's late equalizer earned the home side a reply after Sone Aluko had put Aberdeen ahead.
Kyle Lafferty helped himself to a double as Rangers cruised into the last four with an emphatic victory afteer Steven Whittaker's opener was cancelled out by Rocco Quinn.
Lafferty restored the home side's advantage and Spanish youngster Aaron celebrated his first start by converting from the penalty spot.
Steven Davis then netted early in the second half before Lafferty had the final say with Rangers' fifth, leaving injury-ravaged, 10-man Accies reeling.