Todor Aleksiev added 13 in the 32-30, 25-20, 25-19 victory for the Bulgarians, who dropped only one of five preliminary round matches.
Ivan Zaytsev had 15 points for Italy, which finished the opening round 3-2 for a spot in the quarterfinals. Argentina and Poland also advanced.
The top four teams in each six-team pool move on to the knockout round. The top finishers in each pool face the fourth-place finishers in the opposite pool, while the other matches are determined by drawing lots.
The defending Olympic champion U.S. men had already made the quarterfinals because of three earlier victories in the round, but would clinch the top spot in their pool with a victory against Tunisia in a late match Monday.
The ninth-ranked Bulgarians have been the surprise of the preliminary round because the team came to London in such disarray.
After Bulgaria earned an Olympic berth at a qualification tournament in Sofia, the coach and a top player suddenly resigned to protest their country's leadership of the sport.
Coach Radostin Stoychev and spiker Matey Kaziyski have called for the resignation of Bulgarian federation chief Dancho Lazarov.
Nine players on the 12-man team are first-time Olympians.
"We have created this really good climate among all the players," coach Nayden Naydennov said. "That's why we are playing so well, they are a really good team."
The biggest upset Monday came in the first match of the day, when No. 22 Australia surprised No. 3 Poland 3-1 (25-21, 25-22, 18-25, 25-22). Travis Passier's ace proved the match-winning point and the Volleyroos earned a standing ovation from the Earls Court crowd.
Poland had already qualified for the quarterfinals, but the loss kept them from clinching the top seed.
"We lost control in the beginning and we were not really fighting," Poland coach Andrea Anastasi said. "I have no explanation."
Poland has been on the upswing since hiring Anastasi early last year and the team won the recent World League, beating top-ranked Brazil three times in the early round and again in the finals.
Poland, which won the Olympic gold medal in 1976, finished fifth in Beijing.
The Volleyroos, making their first-ever appearance in Olympic volleyball, needed winless Britain to defeat Argentina in an afternoon match to advance. But the eighth-ranked Argentineans defeated the hosts 25-18, 25-18, 25-15.
Russia defeated Serbia 3-1 (25-15, 25-20, 25-17) to secure a spot in the quarterfinals.