The scuffle broke out moments after Tui Kamikamica crossed over late in the first half, as the Storm enforcer burst onto a Harry Grant short ball from close range.
Storm playmaker Cameron Munster then gave Ogden a condescending pat on the head, triggering the Bulldog to fire back with a wild shove.
That saw big Asofa-Solomona jump into the fray with a swinging arm before the referee sent Ogden and Asofa-Solomona on their way.
“So it’s 12 on 12 … Ofahiki Ogden and Nelson Asofa-Solomona will sit and watch for the next 10 minutes of game time,” said Fox League commentator Warren Smith.
“Ofahiki Ogden has taken the bait from Cameron Munster … and then Nelson Asofa-Solomona did something a bit silly himself.”
Bulldogs great Braith Anasta was amused by Munster’s antics.
“He threw the bait out there, didn’t he, Cam Munster?” Anasta said.
“And two of the big forwards have paid the price. He’s a cheeky five-eighth.”
The incident was a minor inconvenience for Craig Bellamy’s Storm, who motored away to the finish line in a dominant display in Sydney.
Meanwhile, Trent Barrett can be pleased with the progress of his squad, who at times had the reigning champions under pressure.
The Bulldogs also broke a drought of three scoreless games as they piled on an unexpected 18 points.