Terziev headed home his first goal for the club with two minutes remaining as the Bulgarians claimed a famous Group B point at Stadion Vasil Levski on Wednesday.
There was an early warning sign of what was to come for the English side when Dani Abalo capitalised on a dreadful error from under-fire goalkeeper Simon Mignolet to put Ludogorets in front inside five minutes.
But after some comical defending ensured Rickie Lambert marked his first start in this competition with a goal, Liverpool appeared to have turned the tables when Jordan Henderson swept home at the end of a fine move just before half-time.
The poor defending that has plagued Liverpool throughout this campaign reared its head again, though, as an unmarked Terziev nodded home a well-worked corner at the back post two minutes from time.
Terziev's intervention did not change the fact Liverpool can reach the last 16 by beating Basel at home in matchday six, although they would have expected to end their recent slump against competition rookies Ludogorets.
The Bulgarian team, meanwhile, must overcome champions Real Madrid - who have won all five games so far - to have any chance of going through.
The Premier League side endured a nightmare start as the home side took an immediate lead thanks to an error from goalkeeper Mignolet.
The Belgian failed to hold on to a Fabio Espinho's 20-yard strike that was straight at him, gifting prowling striker Abalo the simplest of tap-ins.
Yet seeming to show pity on their beleaguered opponents, Ludogorets gifted Liverpool a way back into the game five minutes later.
Lambert was the beneficiary, capitalising on indecision in the hosts' defence to nod beyond onrushing goalkeeper Vladislav Stoyanov and into the corner.
The Bulgarians responded impressively, however, as they continued to press forward with confidence.
An error-strewn game nearly brought another costly one as Kolo Toure turned Abalo's cross narrowly past his own post.
But Liverpool regrouped thereafter and took the lead thanks to a superbly worked goal eight minutes before half-time.
Raheem Sterling was the architect, sending a pin-point low cross to the far post - where Henderson burst in and expertly lobbed Stoyanov.
Ludogorets were not able to begin the second half how they did the first, although they enjoyed the majority of the possession.
Espinho had the best chance of the early exchanges, curling a 20-yard free-kick harmlessly over the crossbar.
Liverpool continued to invite pressure, though, with Marcelinho's long-range effort deflected just wide off Joe Allen.
There was a palpable sense of tension in Brendan Rodgers' side's play as the final whistle drew closer, especially when Sterling hit straight at Stoyanov when one-on-one with the shot-stopper.
And that miss was to prove incredibly costly as Svetoslav Dyakov flicked on a corner to leave Terziev with an easy task and heap further misery on Rodgers.
