The Belfast side gave as good as they got before losing Seanan Clucas to a 52nd-minute red card and then missed two excellent chances to open the scoring at Fir Park.
But O'Donnell set up Lang to net in the 58th minute and the Scotland full-back sparked a goal spree with a thunderous long-range strike in the 72nd minute.
Liam Polworth and Tony Watt both scored from rebounds in the subsequent six minutes to subject Glentoran to a harsh scoreline and put Motherwell into the second qualifying round.
Hours before kick-off, Motherwell sold their most impressive player in a slow start to the season, David Turnbull, in a potential £3.25million deal to Celtic.
They had a ready-made replacement in Polworth, who had a successful debut campaign while Turnbull was recovering from knee surgery.
Robinson made a tactical switch after derby defeat by Hamilton left them with two points and two goals from five Scottish Premiership games.
The former Northern Ireland international moved to a 3-5-2 formation with Liam Grimshaw brought in at wing-back and Long earning a recall to start up front with Callum Lang.
The visitors included former Well midfielder Gael Bigirimana and they forced some early corners before Long came close on the break.
The striker then forced the first save when his deflected volley was well-stopped by Gibraltar goalkeeper Dayle Coleing following Polworth's corner.
The visitors were rewarded for their enterprise with a number of chances. Marcus Kane had a shot saved following a poor defensive header from Declan Gallagher, Paul O'Neill's deflected effort spun wide with Trevor Carson wrong-footed, and the Northern Ireland goalkeeper made a brilliant save to keep out Rory Donnelly's close-range diving header.
Motherwell were being limited to half-chances with O'Donnell, Long and Allan Campbell being denied and the hosts had another let-off before the break when Clucas shot wide after Grimshaw had lost possession.
Clucas had earlier been booked for a full-blooded sliding tackle on Ricki Lamie and he was off after another poor challenge on O'Donnell.
The 10 men soon had two good chances. Christopher Gallagher beat Grimshaw to the ball and delivered a low cross which Paul O'Neill fired over from six yards. McDaid then sent a free header just wide from Bigirimana's corner.
Motherwell soon calmed the nerves of Robinson and their absent fans. Lang pounced on a loose ball and exchanged passes with O'Donnell before beating the keeper with a deft touch.
Robinson brought on winger Sherwin Seedorf for the struggling Grimshaw in a change devised before the opener and the game opened up.
O'Donnell fired into the roof of the net from 30 yards before Polworth nodded home three minutes later after Long's effort had been parried.
Watt then tapped home following Campbell's blocked shot and Lamie hit the bar from long range before Long headed his first goal of the season from Watt's cross in the 87th minute.
The visitors got off the mark in stoppage-time when McDaid converted a penalty after sub Harry Robinson's foul.