The ads, for the Homescapes and Gardenscapes games, both come from developer Playrix.
They showed a game where users pull pins in a specific order to solve a puzzle - though the actual games had totally different "core gameplay".
The ASA said the ads should not be used again.
In recent years, a number of mobile games have used ad videos that show puzzle game mechanics they do not use - or barely use - prompting complaints from gamers.
Some mobile game developers "are actively targeting consumers that are more likely to pay for in-app purchases, or sit through a higher number of ads," explained Matthew Bailey, a games analyst at Omdia.
"It would not be surprising for a publisher to target certain types of gamers with ads featuring the more competitive and problem-solving elements of their title, even if they don't make up the bulk of gameplay," he said.
"However, an increasing number of gamers are becoming annoyed with irrelevant, misleading and badly implemented mobile game ads."
Homescapes and Gardenscapes both use the same core gameplay loop: a home or garden needs to be renovated, and players earn the resources they need by playing a "match three" type game - similar to other popular games such as Bejewelled or Candy Crush.
Both Homescapes and Gardenscapes are hugely popular, with more than 100 million app installs each from the Google Play store.
But the games have often used ads that show a multiple-choice type puzzle to avert a catastrophe, or, more recently, the pin-pulling puzzle type.
Two Facebook ads for Homescapes and Gardenscapes, from March and April this year, were referred to the ASA for being misleading.
Despite a brief warning at the bottom of the video that "not all images represent actual gameplay", the ASA sided with the seven people who complained.
One BBC reporter, however, said they had seen the offending ads pop up since the judgement was handed down.
In its submission, Playrix said that the type of gameplay in the ads was, in fact, in their games.
But out of thousands of levels of gameplay, there were only 10 such mini-games in Homescapes in April 2020, it said, and the mini-games in the ads were only available every 20 levels or so.
Playrix also told the ASA that "most users" stopped playing near the start of the game. In April, when the offending ads ran, those mini-games were on "distant levels only", the ASA said - meaning most players would never see them.
The company has since changed the game so these mini-games appear closer to the beginning.
"We understood users would play a significant amount of content which was of a different style in order to access the gameplay featured in the ads," the ASA said in its ruling.
"Because the ads were not representative of the games they were purported to feature, we concluded that they were misleading."
It ruled the ads must not appear again - and told Playrix to make sure ads represented its games in future.
Games analyst Matthew Bailey said that "artistic licence" had long been used with game ads, citing 1990s adverts where the cover art was far more impressive than the game graphics.
But the difference now is that devices are advanced enough to be able to show users that the game is like - and developers are sometimes choosing not to.
"The ASA's recent ruling on the topic will send an even stronger message to other game makers about their use of misleading ads," he warned.