Orri Steinn Óskarsson scored twice before Mikael Ellertsson added a late third as Iceland recorded their second win of the campaign.
Óskarsson breaks Bulgaria resistance
Iceland dominated the contest and eventually opened the scoring in the 37th minute.
Óskarsson found the breakthrough before adding his second goal in the 60th minute to put the hosts firmly in control.
The Real Sociedad forward's double took his tally to two goals in the match and gave Iceland a comfortable advantage heading into the final stages.
Ellertsson seals comfortable victory
Bulgaria were unable to find a way back into the contest as Iceland continued to control proceedings.
Mikael Ellertsson completed the scoring in the 90th minute, giving Iceland a three-goal cushion and confirming another important victory in their Nations League campaign.
Iceland move top of Group C4
The victory takes Iceland to seven points from their opening three matches.
Estonia are second on five points after their 1-0 victory over Luxembourg in the group's other fixture, while Luxembourg have three points and Bulgaria remain on one.
Iceland had previously drawn 1-1 with Estonia before defeating Luxembourg 3-0, meaning Saturday's victory maintained their unbeaten start to the campaign.
• Iceland: Orri Steinn Óskarsson 37', 60', Mikael Ellertsson 90'
• Bulgaria: No goals
Iceland will next travel to face Estonia on Tuesday, 6 October, as they look to strengthen their grip on top spot in Group C4.