Former Northern Ireland international winger Keith Gillespie played for Ferguson at Man Utd in the 1990s.
Jamie Mulgrew ran unchallenged to hit Linfield's third on 50 before Keith Gillespie's reply on 63.
Keith Gillespie then put a volley wide for the Glens before Fitzgerald's breakthrough score.
BBC: Glentoran beat Linfield on away goals in quarter-finals
Keith Gillespie of Northern Ireland and Ivan Woods of Malta were sent-off as tempers flared late on.
Keith Gillespie was denied by another Cech save while David Healy blazed wide in the final minute.
Michael Halliday could not believe that Keith Gillespie will be running down the wing and crossing balls for him.
Afterwards, Glentoran's former Northern Ireland star Keith Gillespie said they had been amazed when the penalty was awarded for handball.
He volleyed over wildly at the far post after Keith Gillespie's cross had evaded a succession of West Ham defenders.
BBC: SPORT | Football | Premiership | Sheff Utd 3-0 West Ham
Winger Keith Gillespie was left out of the original squad for the game after being released by Championship side Sheffield United.
The Glens were without winger Keith Gillespie, who failed a fitness test before the game while O'Hare returned to the Coleraine goal.
Keith Gillespie is also back after recovering from injury and stands a good chance of starting because Jon McCarthy is out with a broken leg.
He was again wayward towards the end of the first half but right on the stroke of half time there was relief for the home fans when Aranalde brought down Keith Gillespie.
Maik Taylor (Fulham), Roy Carroll (Wigan), Aaron Hughes (Newcastle), Mark Williams (Watford), Danny Griffin (St Johnstone), Ian Nolan (Sheffield Wednesday), Colin Murdock (Preston), Pat McGibbon (Wigan), Kevin Horlock (Manchester City), Keith Gillespie (Blackburn), Damien Johnson (Blackburn), Michael Hughes (Wimbledon), Jim Magilton (Ipswich), Jeff Whitley (Manchester City), Danny Sonner (Sheffield Wednesday), Steve Lomas (West Ham), James Quinn (West Brom), Adrian Coote (Norwich), David Healy (Manchester United), Stephen Robinson (Bournemouth).
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