The Porto forward was in the squad as a replacement for Neymar, who had Copa Libertadores commitments, but gave national coach Mano Menezes food for thought with his first-half double.
An own goal by Niki Zimling added to their tally, with Denmark's only reply coming from the boot of Nicklas Bendtner.
Hulk took just seven minutes to open the scoring with a powerful long-range shot which dipped beneath the dive of goalkeeper Thomas Sorensen.
Brazil were two ahead four minutes later when Oscar's cross into the box was turned into his own net by the unfortunate Zimling.
Denmark's afternoon deteriorated further when both Sorensen and midfielder Lasse Schone were substituted with injuries, to be replaced by Stephan Andersen and Thomas Kahlenberg.
And Wolfsburg player Kahlenberg had the first real chance of the afternoon for the Danes with a header which was well saved by goalkeeper Jefferson.
Brazil continued to dominate, though, and they were 3-0 up six minutes before half-time. Oscar sprinted into the area before laying the ball off to Hulk, who slipped a low shot into the net.
With Menezes making a spate of changes at the start of the second half, the South Americans began to relax, allowing Denmark to press forward.
Their persistence paid off after 70 minutes when Zimling's low cross was tapped in by Bendtner.
The win was ideal preparation for Brazil's upcoming Olympics campaign, with further friendlies scheduled against the United States, Mexico and Argentina.
Denmark will face Australia next Saturday before opening their Euro 2012 challenge against Holland on June 9.
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