Stanislav Manolev had given the hosts the lead before Osvaldo's double put Italy ahead and it was left to Bulgaria's lively midfielder Milanov to earn a share of the points with a goal midway through the second half of the Group B clash.
"I didn't expect Bulgaria to play like this but you see that all teams have a difficult periods and Italy are no exception," said Italy coach Cesare Prandelli.
Bulgaria coach Luboslav Penev said: "We totally outplayed Italy, one of the best teams in the world, not [just] in Europe but they scored two lucky goals.
Expressing his frustration with the decisions of English referee Martin Atkinson he added: "There were three or four handballs in their penalty area. It was very difficult for the referee to award us free-kicks."
The Bulgarians, who failed to score in their four home Euro 2012 qualifiers, almost went ahead when defender Ivan Ivanov's curling shot from Emil Gargorov's free-kick forced a spectacular save by Italy goalkeeper Gianluigi Buffon.
The AS Roma player, who was not part of the Italy squad at Euro 2012 where they lost in the final, netted from close range in the 36th minute from the unmarked Claudio Marchisio's clever assist to level the scores with Italy's first shot on goal.
"It's a memorable evening for me and I'm happy or at least half-happy with my two goals because the result was not satisfactory," said Osvaldo.
"I usually score beautiful goals while those were scruffy, but they are worth as much as the others.
"It was a difficult game, at times we were a bit slow and we didn't play the way we normally play."
