A double from Josip Ilicic and a curling effort from Marcos Tavares put Hibs three goals behind before the hour mark and the score only threatened to get worse despite a tactical switch from John Hughes.
Hughes left his two most dangerous players out of his starting line-up with Colin Nish the lone frontman and both Anthony Stokes and Derek Riordan on the bench.
However, his team were second best throughout a difficult night against a side who have scored five goals without reply in their opening two league games and dispatched Videoton of Hungary 3-1 on aggregate in the previous round.
Right-back Michael Hart and Dutch midfielder Edwin De Graaf were handed competitive debuts with David Wotherspoon employed on the left of a five-man midfield.
Graham Stack won the battle for the gloves ahead of Graeme Smith and the Irishman showed his worth early on as the Hibs defence struggled in the absence of Sol Bamba, who did not travel after returning late from his post-World Cup break.
John Rankin had a shot comfortably held but Hibs were otherwise struggling to settle and Stack blocked brilliantly from Dalibor Volas in the 17th minute.
Maribor continued to dominate and Tavares blasted a 30-yard strike just wide before Stack tipped away another close-range effort from Volas.
A number of Hibs players were finding it difficult to keep their footing in the wet conditions and the Edinburgh side fell behind in the 31st minute.
Ilicic appeared to be outnumbered inside the box but he found space before blasting the ball in off the underside of the bar.
Hibs improved just before the interval, twice coming close after enjoying some better possession.
Liam Miller collected a short pass from Wotherspoon before striking a swerving 25-yard effort that was pushed away superbly by the outstretched hand of Maribor goalkeeper Marko Pridigar.
Chris Hogg's header was then cleared from a crowded goalmouth after John Rankin delivered the resulting corner.
Nish had an effort blocked early in the second half but Hibs fell further behind in the 52nd minute when Ilicic brilliantly chipped Stack from 20 yards after Wotherspoon had lost possession.
However, Hibs had the right to feel aggrieved as the youngster looked to have been caught in the ankle by Armin Bacinovic's sliding tackle.
Stack saved Hibs from further punishment when he got down brilliantly to his left to push away an effort from Tavares.
But Maribor moved further ahead on the hour mark when captain Tavares curled high into the corner from inside the box.
Hughes made the changes the Hibs fans were calling for in the 68th minute when Stokes and Riordan were sent on to rescue the tie in place of Nish and Kevin McBride.
Hibs began to enjoy more of the ball in the opposition half but they never looked like getting the away goal that would have left them with some hope to cling on to.
Rankin's dangerous inswinging corner was beaten away by Pridigar and the hosts might have done better from the resulting counter-attack.
Danny Galbraith replaced Wotherspoon but Maribor finished in the ascendancy as Hibs survived several dangerous crosses.