The pupils, who sat the Higher in religious, moral and philosophical studies (RMPS), were given the wrong marks when incorrect data was entered into a computer.
Education secretary Michael Russell said he regarded the error, which was first spotted by a school, “very seriously”.
The SQA admitted that the papers of 3,084 candidates who sat the Higher RMPS exam were reviewed after the school complaint.
As a result, 34 candidates received upgrades and a personal apology from the exams body.
In 2000, thousands of Scottish pupils were left with missing or inaccurate results following administrative problems at the SQA. Chief executive Ron Tuck quit the authority and Jack McConnell was brought in as education minister to resolve the fiasco.
In 2007 a mistake in a letter sent to pupils by the SQA contributed to thousands receiving their results late, while last year almost 30,000 pupils received exam results a day early after a texting gaffe.