The Gunners had picked up just one point from their last four matches but made the perfect start inside two minutes when Theo Walcott picked up on a poor clearance by the Rovers defence, the England international sliding in a low cross for Van Persie to tap home.
Arsenal continued their domination but couldn't find a second and were surprisingly pegged back when Morten Gamst Pedersen struck home a marvelous freekick from the edge of the box.
However, Blackburn weren't on level terms for long, Van Persie restoring Arsenal's lead seven minutes later with a carbon copy of his first, Walcott pulling it back for him to strike home.
Alex Oxlade-Chamberlain then made it 3-1 two minutes later, Van Persie turning providing to slide the ball through for the 18-year-old who rounded Rovers keeper Paul Robinson before slotting home.
Blackburn's miserable first half was compounded when Gael Givet was shown a straight red card for a lunging challenge on Van Persie.
The second half didn't get much better for Rovers when Mikel Arteta added a fourth six minutes into the second half, a sweet strike from the edge of the box proving too good for Robinson.
Oxlade-Chamberlain continued the rout three minutes later when Walcott skipped past two defenders before setting up his compatriot for the fifth.
Van Persie then completed his hat-trick just after the hour mark when the Dutchman picked up Francis Coquelin's cross before driving the ball into the back of the net.
Arsenal's brilliant day was then rounded off by Thierry Henry in stoppage time, the Frenchman picking up on Grant Hanley's mistake before playing a one-two with Van Persie, his shot taking a deflection on its way in.
The result puts Arsenal just two points behind fourth-place Chelsea while Blackburn remain firmly rooted inside the bottom three.