The ad features crowds cheering while the pirate races a carriage through a square, discovers treasure in a cave, strips off and swims in the sea.
A viewer complained that it linked alcohol with daring, toughness and aggressive behaviour.
Diageo responded by claiming that the captain was fully in control in all scenes and that they were neither daring nor dangerous.
It added that it took care to ensure the scenes featuring the pirate riding a horse and swimming did not feature any alcohol and were unconnected with any alcohol consumption to avoid them being portrayed as potentially dangerous if carried out after consuming alcohol.
It said the few images of alcohol appeared later in the ad and were “contextualised in celebratory settings”.
But the Advertising Standards Authority upheld the complaint and said the ad must not appear in its current format again.
It said: “We noted that some shots in the ad highlighted the buccaneer’s playful and on occasion provocative personality, but also noted that he was shown driving a carriage at speed, searching a cave for treasure and emerging from the sea having apparently dived from his ship.
“We considered that those actions and the settings shown in the ad would be associated with buccaneers and seafarers renowned for drinking rum, and for their disregard for authority and the well-being of themselves and others.
“Therefore, we concluded that, the depiction of the character and his actions, especially when placed alongside the slogan “LIVE LIKE THE CAPTAIN”, in an ad for rum, linked alcohol with daringness and toughness.”
The ASA dismissed another complaint that suggested the ad linked alcohol to social success.
Meanwhile Heineken dodged a rap on the knuckles after successfully arguing that its ad for Strongbow did not imply that drinking alcohol could be used to overcome problems, enhance personal qualities and improve performance.
The ad featured three men finding inner strength to overcome such problems as scoring a penalty past a brick wall, potting a ball on a snooker table that turned into a fiery chasm and delivering a best man speech when the words had magically fallen off the page.
Heineken said the ad featured vignettes of three friends who faced every day challenges and that the self-imposed pressures in their minds developed into a humorous and an obviously fantastical nature.
It said the ad showed each of the men finding the inner strength to push on to complete their chosen task as the scenes snapped back to reality.
It added that the men were then shown raising a pint of Strongbow in celebration to each other as a reward, after their tasks had been completed, and that the closing scenes of celebration were all in scenarios where it would be acceptable, and not unusual, to consume alcohol.
The ASA agreed and said no further action was required.