Strikes by Callum Lang, Stephen O'Donnell, Liam Polworth, Tony Watt and Chris Long saw the Steelmen through to next Monday's draw for the next round. The goals followed the early second half dismissal of Glens' Seanan Clucas.
With recorded Well Bois singing booming out of the Fir Park PA system in the Phil O'Donnell Stand from the off, the hosts started with purpose on the lush park.
The first chance for Motherwell on seven minutes saw a quick break from a corner leading to Polworth and Lang setting up Long who shot powerfully but wide of the far post from 18 yards.
The first booking on nine minutes saw Clucas yellow carded for a late challenge on Ricki Lamie.
A Polworth corner then saw Long's volley blocked by a defender, before another Polworth flag kick from the other side saw a Bevis Mugabi header thwarted.
A long free-kick delivered by ex-Motherwell ace Gael Bigirimana into the box was headed out by Declan Gallagher to away defender Marcus Kane whose shot was comfortably saved by home keeper Trevor Carson.
Glentoran came very close to scoring on two occasions just before the half hour mark. Firstly Paul O'Neill's shot was deflected wide with Carson wrong footed and beaten, before from the resultant corner Ruaidhri Donnelly's point blank header was smartly stopped by Carson.
Motherwell - missing the goal threat of David Turnbull who joined Celtic earlier in the day - created a chance when Campbell set up Stephen O'Donnell whose shot was saved by away keeper Dale Coleing. The custodian was soon in action again to save a Long shot.
A misplaced Liam Grimshaw pass in midfield was pounced upon by Glentoran but Robbie McDaid shot weakly wide.
'Well came close when Campbell's shot was deflected over after good work by Polworth and O'Donnell.
The visitors were reduced to 10 men on 52 minutes when Clucas was sent off for a second bookable offence. But the Northern Irish side continued to threaten with Christopher Gallagher's cross turned wide by Paul O'Neill. O'Neill then missed another fine chance before Motherwell broke to the other end where a Grimshaw cross from the right was sent wide by Lang.
Motherwell went ahead on 57 minutes when Lang turned in an O'Donnell cross, much to the relief of all the Motherwell fans watching on TV sets and laptops.
A stunning long range shot by O'Donnell on 72 minutes - following a pass inside by substitute Sherwin Seedorf - then put the Steelmen 2-0 up.
It was soon 3-0 Motherwell when Liam Polworth headed in from point blank range after Long's initial shot had been parried by the keeper.
Tony Watt scored Motherwell's fourth from close range after Allan Campbell shot was parried - 4-0 after 77 minutes.
O'Hara's 84th minute rasper from 20 yards was deflected over.before Lamie volleyed against the bar following the resultant corner.
But it was soon 5-0 Motherwell when brilliant wing play by Watt saw his cross headed in by Long.
Glentoran got a consolation goal late on when McDaid thumped home a penalty awarded for Polworth's foul.
Motherwell: Carson, Grimshaw (Seedorf 60), Lamie, Campbell, O'Hara, Mugabi, Polworth, Lang (Watt 69), Gallagher, O'Donnell (Robinson 81), Long.
Referee: Bram Van Driessche