Fans were not allowed into the ground in Zagreb to witness Ante Cacic's debut as coach following a racist incident in their 1-1 home draw against Italy in June. Croatia also had a point deducted.
Saturday's result left Croatia, who have claimed at least a playoff spot, third with 17 points from nine games, two behind Norway, who beat Malta 2-0, and four adrift of leaders Italy, who booked a place at the finals with a 3-1 win in Azerbaijan.
Croatia, who have only once failed to reach the European Championship since independence in 1991, visit Malta in their final qualifier while Norway travel to Italy on Tuesday.
The third-placed finishers will still have a chance to make it through to the finals via a two-legged playoff.
"This was just one step. We have to win in Malta to make these points valuable," said Cacic, who was concerned about the weather conditions for their next match. "It will be 30 degrees (Celsius) in Malta, it will be tough, but we are ready."
Croatia were back on top form under Cacic, who last month replaced the sacked Niko Kovac, as they bounced back from disappointing performances in their previous two games.
"We scored early, were more motivated than Bulgaria and, in the end, Croatia has more quality," he said. "With this passion, we can even go to the playoffs in good spirits."
Ivan Perisic, the group's top scorer, put Croatia ahead inside an eerily silent stadium normally known for its deafening atmosphere with his fifth goal in the campaign following a fine through ball by Luka Modric after 88 seconds.
Nikola Kalinic, replacing the injured Mario Mandzukic, almost doubled their lead a few minutes later, they had a goal wrongly disallowed for offside and Bulgaria defender Georgi Terziev rattled his own post attempting a panicked clearance.
The lively Ivan Rakitic did make it 2-0 with a low right-foot shot after playing a one-two with Kalinic three minutes before the break. Kalinic then completed the scoring from close range in the 81st minute following a precise cross from Perisic.
Croatia substitute Duje Cop was sent off for a reckless challenge on defender Strahil Popov in the closing stages.
(Reporting by Angel Krasimirov; Editing by Ken Ferris/Mitch Phillips)
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