The £2.6million summer signing netted just his third goal of the campaign with only seconds left to cancel out David Mooney's second-half header.
An upset looked on the cards when Mooney nodded in his ninth of the season with 12 minutes to play - and the Os were worthy of their lead.
But it was snatched away from them three minutes into stoppage time when German striker Proschwitz headed in Tom Cairney's cross.
The Os, who reached the last 16 of the competition two seasons ago, signalled their positive intent with an early Dean Cox effort from the edge of the box that flashed just wide.
The visitors went close again after 16 minutes when Kevin Lisbie went past two defenders in the box before shooting wide. And they were denied by Eldin Jakupovic's excellent save from Leon McSweeney's long-range drive soon after.
There were two further chances before the break for the Os, Lloyd James nodding Cox's left-wing corner wide and Lisbie firing over the bar from the edge of the box.
Hull boss Steve Bruce switched to a 4-4-2 formation in a bid to offer a more potent attacking threat in the second half. It almost paid dividends within three minutes of the restart, but Alex Bruce failed to keep his header down after connecting well with Cairney's delivery.
But it was Orient who should have taken the lead with 54 minutes gone. Lee Cook raced through and had the goal at his mercy but could only shoot straight at Jakupovic.
They were almost made to pay two minutes later as Paul McShane rose highest to meet Cairney's corner but cleared the bar with his header.
Crosses from wide areas continued to be the hosts' most promising outlet, a fact underlined by Andy Dawson's 70th-minute delivery which McShane headed powerfully at goal to force a smart stop from Jamie Jones.
Orient took the lead with 12 minutes remaining when Cox delivered from the right for Mooney to head home from six yards out.
Lisbie headed wide in Orient's next attack and Proschwitz volleyed off target late on as it looked like City's final chance had gone. But Cairney had one more pinpoint cross to deliver and Proschwitz was on hand to provide the decisive touch.