The Clarets looked to be heading for a draw until Brownhill delivered the sting in the fourth minute of added-on time.
Burnley had to come from behind after Callum Lang had given Pompey a lead against the run of play in the first half.
Jeremy Sarmiento levelled just two minutes after coming on as a second-half substitute, the Brighton loan signing firing inside the far post with a curling effort from the left side of the area.
Portsmouth had done their best to eat up the clock with a series of time-consuming injuries and substitutions a, before Brownhill struck.
Clarets boss Scott Parker insisted the ball fell to the right man in the dying minutes given the midfielder’s experience and composure in crunch moments.
“He gives you every bit of that experience and composure,” said Parker.
“He understands and has the nous around the football pitch and this division.
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