A header from Shane Duffy in the 93th minute saved the Republic of Ireland from defeat on Stephen Kenny's first outing as manager.
Having conceded 11 minutes after the restart, when Todor Nedelev played to Bozhidar Kraev in between Duffy and John Egan, firing through Darren Randolph’s legs.
The home-side's form improved following the goal, but Ireland remained the stronger looking outfit.
The return of Robbie Brady brought some welcome experience to the field, with Brady's corner to Duffy providing a solid chance for Ireland, but did not manage to find the back of the net.
The boys in green will ponder some missed opportunities in the first half, with Aaron Connolly squandering a good 13th-minute chance for the visitors when he fired wastefully across goal from a difficult angle after dispossessing defender Kristian Dimitrov with Adam Idah and Callum O’Dowda better placed in the middle.
Another chance came for Ireland just before the break, with O’Dowda missing the target after a strong cross from Enda Stevens in 45th-minute.
Meanwhile, in the evening's other Group H fixture, Wales saw off the challenge of Finland with a goal from Kieffer Moore in the 80th minute.
Earlier, Moore headed home Daniel James’ cross after four minutes but their celebrations were swiftly cut short for a push on Finland defender Leo Vaisanen.
Kenny's side will now look forward to their fixture against Finland on Sunday in the Aviva.
