Despite threatening a rout by scoring so early, Bulgaria struggled to build on that advantage, but it was not for the lack of trying as Galabinov struck the crossbar on 26 minutes.
Malta looked dangerous on the counter-attack at times, but only had the one shot on target to show for their first-half labours.
Having opened the scoring early in the first half, Malta gave their hosts a taste of their own medicine by equalising just three minutes into the second half.
The Bulgarians could, and perhaps should, have re-established the lead shortly before the hour mark when Alexandrov was denied by Hogg in their best chance of the half.
Popov - who had earlier struck the crossbar - saw his night get far worse. Having conceded an earlier penalty, he then spurned the chance to atone for that incident by missing from the spot on 76 minutes to compound a miserable night for the veteran striker.
Bulgaria remain fourth in Group H, six points behind co-leaders Italy and Croatia.