A far from full-strength Hoops side fell behind to Marko Pjaca's strike after 14 minutes before goals from Kris Commons and Stefan Scepovic had the visitors ahead.
However, Pjaca levelled with a deflected shot and he claimed his hat-trick five minutes after the break after the lead had been regained through Marcelo Brozovic, as Celtic rocked.
Dinamo defender Josip Pivaric put through his own goal with nine minutes remaining and Scepovic almost grabbed a late equaliser with a header.
However, when the final whistle sounded, Ronny Deila's side were left with eight points from six games.
The draw for the last-32 is next week and the Celtic boss admitted his side would need to improve if they were to go further in the tournament, a prediction confirmed against Dinamo.
However, the Scottish champions should be back at full strength by the next round in February, notwithstanding any players who come in or leave during the transfer window.
The threat of a suspension meant skipper Scott Brown was left in Glasgow along with James Forrest, who requires an increase in his fitness levels.
Ineligible striker John Guidetti also dropped out while midfielder Charlie Mulgrew and Jason Denayer were out injured and Mikael Lustig continues his recovery from a hamstring injury.
Consequently Scepovic and winger Mubarak Wakaso were given rare starts with wide-man Callum McGregor and Commons drafted in.
Dinamo's dismal European form - they could not finish above third - resulted in a sparse home crowd which gave an eerie feel to an austere stadium.
There was a flare displayed among the 1,000 or so Hoops fans as the game got under way, which may have UEFA ramifications, but they made themselves heard in the early stages of what turned out to be an open if error-riddled first-half.
In the 10th minute, after Dinamo goalkeeper Eduardo had made a decent save from Commons, Dinamo striker El Aarbi Hilal Soudani had the ball in the Celtic net - but the flag was up for offside.
The home side took the lead when a miscued shot from Arijan Ademi landed at Pjaca, who turned inside right-back Adam Matthews before curling the ball low past Parkhead keeper Craig Gordon and into the far corner.
The visitors levelled after midfielder Nir Bitton was fouled by Dinamo skipper Domagoj Antolic 25 yards from goal.
Hoops captain Virgil Van Dijk fired in the free-kick and when the ball came off the defensive wall and looped high into the air Commons was surprisingly left all alone to head it into the net.
There was more joy for Celtic on the half-hour mark when Commons won and took another free-kick from a dangerous position.
His drive crashed off the bar and Bitton headed on to Scepovic who hooked it into the net from close range, the Serb then booked by referee Gediminas Mazeika for his celebration.
Six minutes from the break it was Celtic's turn to be punished for slack defending
Adam Matthews lost possession in his own box when he could have cleared and Pjaca's shot was deflected off Bitton past Gordon, who moments later denied the same player after he again found space in the porous Parkhead penalty area.
Gordon started the second half by making another fine save, this time from Soudani's volley - but in the 48th minute he was beaten by a fine curling shot by Marcelo Brozovic from the edge of the box, after he had taken a pass from Antolic.
When Pjaca drove past Gordon from 20 yards two minutes later it looked ominous for the Hoops, who soon replaced the hapless Matthews with Darnell Fisher.
Celtic steadied themselves and were handed a late lifeline when Pivaric turned an Emilio Izaguirre cross into his net under pressure from Scepovic - who almost levelled with a header minutes from time.
Source : PA
Source: PA