Shamrock Rovers boss Trevor Croley admitted it was a snatch and grab success for his side at Coleraine on Monday night.
An injury time goal from substitue Ciarn Kilduff earned Rovers a quarter-final draw with 2005 champions Linfield next month.
Last night's tie looked set for extra time with Rovers leading through an early Mark Quigley goal but Kilduff rifled the all important second goal as Coleraine's defence failed to clear the danger.
"It's a cruel way to win a game but I thought we deserved it," said Rovers new boss Croley as his side entered the quarter-final draw.
"Coleraine are an excellent side. They showed some real character.
"We were magnificent in the first half and then Coleraine came at us but we saw them off."
Coleraine boss Oran Kearney said: "I don't know if we went to sleep for the winning goal but the ball just didn't clear and against a side of that quality you will be punished. I thought they made a fantastic start and we took time to find ourselves but it was disappointing to concede early."
Rovers, demonstarting a real hunger to impress, took the lead and levelled the tie after only six minutes.
Busy Gary McCabe's tantalising cross from the right left keeper Michael Doherty uncertain about coming off his line for the ball. As he delayed, Mark Quigley outpaced the home defence, ran into the spaceand crashed a volley into the net from six yards.
But Coleraine gradually eased their way into the game. A clever move involving Stephen Lowry and Paul Owens provided Coleriane with their first opportunity after 27 minutes but Lowry could not get direction on his header. As the home side grew in confidence Lowry worked an opening for midfield colleague Ruairi Harkin but Murphy got down low to his right to snatch the ball.
Only the combination of a fingertip save by Doherty and the woodwork saved Coleraine from falling further behind in the second half. James Chambers smashed a right foot shot towards goal from 25 yards out. Doherty extended himself to some how guide the ball onto the crossbar.
Rovers finished with a late flourish and it was lef to Kilduff to punish the tiring Coleraine defence from 15 yards, drilling his shot beyond keeper Doherty.
Coleraine: Doherty, Canning, Beverland, Ogilby, McIlmoyle, Bradley, Hegarty, Harkin, Lowry, Owens, Jennings (Allen 42). Subs. McVey, Scullion, Watt, Boyce, Tomelty, Shannon (GK).
Shamrock Rovers: Murphy, Sullivan, Powell, Foran, McGuinness, McCabe (Kilduff 69), Quigley, Finn, Chambers, O'Connor (Stewart 77), Robinson. Subs. Oman, McCormack, Rice, Sheppard, Winn (GK).
Referee: Arnold Hunter (Maguiresbridge).