In a first half devoid of many clear-cut opportunities, a Niall McGinn corner looked as though it was destined for the far corner until Mal Smith cleared the danger for the Crues.
James Teelan spurned a big chance for Crusaders in the second half after his strike from an excellent ball into the box by Paul Heatley failed to test Oliver Webber.
It took spot kicks to decide the outcome and Daniel Larmour and Mikhail Kennedy both netted before Jarlath O’Rourke and Philip Lowry’s efforts were saved by Glens keeper Webber.
Sean Murray, Cameron Palmer, Bobby Burns and Junior all dispatched their penalties to give Glentoran a 4-2 victory.
At Taylor’s Avenue, it was Carrick Rangers who progressed to the last eight with a hard-fought 3-2 win over Cliftonville.
The Reds’ Ben Wilson and Rangers’ Ben Tilney netted stunning strikes in a whirlwind start to the tie before the hosts took a 2-1 lead into the break when Curtis Allen made no mistake from the penalty spot.
An own goal from Tilney levelled the score at 2-2 but Carrick had the final say when Danny Purkis fired home with 16 minutes left.
Ballymacash Rangers also booked their place in the quarter-finals, seeing off H&W Welders on penalties after drawing 1-1 in regulation time.
Ballymena United’s interest was ended when they lost 4-3 at home to Knockbreda, Bangor defeated Ballyclare Comrades 4-2 and Dundela were 3-0 winners over Newington.