A Hearts side that finished with 10 men following Scott Robinson's red card held on for a 1-1 draw against Inverness at Easter Road before winning 5-4 on penalties following Philip Roberts' miss.
Michael Ngoo scored on his debut to cancel out Andrew Shinnie's opener and Hearts held on despite Inverness striker Billy McKay getting set up for an open goal before Hearts got players back and Jamie MacDonald saved from Shinnie.
Hearts warned they were in danger of going out of business in November but fans raised £1million to keep the club's head above water and they now have another trip to Hampden to look forward to following last year's thrashing of Hibernian in the William Hill Scottish Cup final.
"It's massive," McGlynn said. "It's a great boost for the fans because there has been a lot of doom and gloom this season. There has been a lot of negativity, and hands up, a lot we have brought on ourselves. But nevertheless it's great for the fans to go back to Hampden. It was great here, they must have seen the fight in the players.
"How Inverness didn't score the opportunity when it was two against one was partly their fault but our players had the fight to get back and stop the ball going in the net.
"We had seven under-21s on that park, five of them came through our youth system, and other players over 21 who came through our youth academy. So we owe a big thanks to everyone who has worked in our youth system. Financially it's a massive boost as well because the football club is not out the woods yet."
Inverness travelled to Edinburgh unbeaten in 10 games and having only lost to Celtic and Motherwell previously this season, and manager Terry Butcher found defeat hard to stomach, although he made a point of congratulating Hearts and McGlynn for his bold team selection.
"We had enough chances to win two or three games but we didn't take them and it's not like us," Butcher said. "It's an unusual feeling because we haven't lost for ages. It still hurts though. I think a fire extinguisher went missing off the wall when I came in. I don't like losing.
"I said to the players I don't want to have this feeling again for the rest of the season if we can. We have had a right kick in the privates and we have to bounce back."
- Sports & Recreation