Ponting, whose team face a huge task to save the test and keep alive their hopes of winning back the Ashes, spent more than a minute remonstrating with Dar after demanding a review of a not out decision against England batsman Kevin Pietersen.
Wicketkeeper Brad Haddin had launched a loud but solo appeal for caught behind, convinced Pietersen, who was on 49, had nicked the ball from quick Ryan Harris.
A review of the decision revealed no "hot spot" where the ball passed Pietersen's bat but a furious Ponting, who was joined by finger-jabbing seamer Peter Siddle, argued long and hard with Dar, prompting jeers from the crowd.
The International Cricket Council (ICC) said in a statement Ponting pleaded guilty to the charge of "arguing or entering into a prolonged discussion with the umpire about his decision.”
"Ricky's actions as captain of his country were unacceptable. A captain is expected to set the example and not get involved in a prolonged discussion with the on-field umpires and question their decision," match referee Ranjan Madugalle said.
"While pleading guilty to the charge, Ricky understood that the discussion went far too long. He apologized for his action and stated that he has nothing but respect for the umpires and his on-field actions were not intended to show disrespect to Aleem Dar or Tony Hill." Siddle declined to comment on the incident.
"It's just cricket," he said, refusing to elaborate when asked if the incident had stemmed from frustration from long spells in the field for little reward.
Pakistani Dar, widely regarded as one of the best umpires in world cricket, later called on the technology to save England's Matt Prior after he was caught behind.
Prior, who was on five, walked but was called back to the crease as Dar consulted the third umpire, whose review of the footage showed bowler Mitchell Johnson had planted his heel on the line and the delivery was a no ball.
Pietersen made just two more runs after the first appeal before falling lbw to the fired-up Siddle but Prior went on to form a formidable partnership with Jonathan Trott.
