The Gunners carved out a number of chances to take the lead but failed to make the breakthrough and were made to pay in the 72nd minute when Kazim-Richards pounced on a rebound to score for Rovers.
And the Championship side produced a spirited defensive performance in the closing stages to hold on for a famous win and pile the pressure on Arsene Wenger ahead of Tuesday's UEFA Champions League clash with Bayern Munich.
Wenger decided to make several changes to his starting line-up and Alex Oxlade-Chamberlain, given a chance to impress in midfield, was soon on the ball as he released Tomas Rosicky down the right only for the Czech winger to clip his attempted cross behind.
Arsenal fans behind the goal at the Clock End called for a penalty when Rosicky's cross hit Scott Dann on the arm as he blocked it behind for a corner, but referee Mike Dean was not interested.
The home side continued to press, forcing a succession of corners. In the 25th minute, Arsenal finally got the delivery right from Rosicky, and Abou Diaby rose to power a bullet header goalwards, which Rovers goalkeeper Jake Kean beat away at full stretch with a magnificent reaction save.
Kean was on hand to palm away a looping header from captain Thomas Vermaelen, fit again following an ankle problem, as the Rovers goal was under siege again.
The best opening came just before half-time when Rosicky slipped Gervinho into the penalty area, but despite holding off the defender, the Ivory Coast forward dragged his shot wide of the post - before dropping to his knees in despair.
Blackburn started the second half brightly and Vermaelen had to be alert as he touched a cross behind with Jordan Rhodes waiting to knock the ball in at the far post.
Diaby flashed a 25-yard effort wide as Arsenal slowly regained momentum, while Rosicky crashed a 20-yard effort off the crossbar and Rovers defender Grant Hanley made an important block as Gervinho cut in from the right.
With 20 minutes left, Wenger had seen enough and made a triple substitution as Theo Walcott, Jack Wilshere and Santi Cazorla replaced Gervinho, Rosicky and Oxlade-Chamberlain.
However, out of nothing, Blackburn snatched the lead as Martin Olsson burst into the left side of the penalty area and drilled the ball goalwards. Wojciech Szczesny parried but Kazim-Richards' scuffed follow-up effort bounced onto the post and in.
Arsenal immediately went on the offensive, but Diaby's effort was charged down and Kean somehow saved a close-range header from Walcott before Olivier Giroud's effort in stoppage-time was blocked as Rovers clung on for a famous win.