Cheerz bar in the High Street and the Mill Inn in Thornhill Road were each handed a £10,000 fine after Sky sought and was awarded permanent interdicts in the Court of Session.
These prevent licensees from breaching copyright by showing Sky programmes without the correct commercial licence.
The court decision also forces the pubs to advertise the ruling in local and trade publications.
Three other Scottish bars faced similar action after Sky investigators visited their premises.
The fines are the latest in a long series of punitive damages awarded to Sky against publicans who fall foul of the copyright rules.
In previous cases this has involved use of foreign decoder devices to get around the Sky-registered system.
The charges levied by Sky are one of the licensed on-trade’s biggest concerns, with some licensees claiming that only the largest and most busy bars can justify the expense.
Sky argues its sports package is a massively popular product that cannot be rivalled and it invests heavily in resources to police”its copyright on key games, visiting hundreds of pubs across the UK every year.
George Lawson, head of commercial piracy at Sky, said: “Illegal broadcasting of sporting events is damaging to the pub industry, which is why we’re committed to protecting Sky customers, who are unfairly losing business due to this illegal activity.”
“There have already been numerous cases this football season of landlords who face hefty financial consequences for this type of fraudulent activity.
“These latest orders demonstrate how seriously the courts take piracy through the large penalty applied, but also through the order to fund advertising, which we hope will help to highlight the consequences of televising Sky’s content illegally.”
Paul Waterson, chief executive of the Scottish Licensed Trade Association, said the SLTA would never condone use of illegal decoders, but added: “Sky is asking more and more for less and less – it lost the Champions League to BT and, while Scottish football is only part of it, a lot of publicans are disgusted by the coverage.
“Some pubs have to pay £10,000 or more a year and while Sky used to be good the quality of service now isn’t there.”