Reform Scotland's study of the quango state also found 200 senior staff with the arm's-length public bodies are paid six-figure wages, with 132 of them - enough to fill every MSP seat at Holyrood - taking home more than a Cabinet secretary.
Reform Scotland said the lack of accountability and transparency among quangos showed the sector was ripe for reform, and recommended scrapping most of them entirely and transferring their work to government departments, councils or independent contractors.
The criticisms were last night echoed by all three major opposition parties at Holyrood, who said the Scottish Government was failing to institute reform when tight budgets meant they should be counting every penny going to quangos.
Successive governments have promised to light a "bonfire of the quangos" to increase efficiency.
Although the SNP has cut numbers by around one quarter since 2007, many of the bodies axed were relatively insignificant, including two dozen Justices of the Peace Advisory Committees.
The new study builds on previous work by the non-party think tank, which found 19 quango chief executives were paid more than the £141,000 a year earned by Alex Salmond and 39 were paid more than the £101,000 of a Cabinet secretary.
Using freedom of information law, Reform Scotland extended its trawl of salaries below chief executive level to uncover the level of pay of all senior staff at the public bodies.
The highest paid boss was Douglas Millican, chief executive of Scottish Water, who is on £240,000.
Three of his immediate underlings were also paid more than the First Minister.
Scottish Enterprise chief executive Lena Wilson was paid around £210,000. But the most lucrative sector by far was health, with 37 NHS board chief executives and senior mangers being paid more than Salmond.
The health figures were limited to managers, and did not include clinical staff; many GPs and consultants also earn more than £100,000.
In total, Reform Scotland identified 686 quango staff in 2012-13 who had been paid more than the £57,521 earned by an MSP.
Of these, 132 earned more than the £100,748 salary of a Scottish Cabinet secretary.
Because only 61 of the 72 quangos who were asked for their salary figures replied, the true figures are probably higher.
The think tank's report said although some of the salaries might be justifiable, it was "difficult to argue that any public sector salary should be higher than that of the person running Scotland, the First Minister".
Describing quangos as unaccountable either to voters or the Scottish Parliament, it recommended scrapping all the arm's-length bodies, with the exception of tribunals and Children's Panels.
It said the quangos' work should either be taken in-house to government departments; or transferred to councils; or the quangos should be "turned into genuinely autonomous bodies which could then enter into an open and transparent contractual relationship with government to undertake certain functions".
A Reform Scotland spokesman denied that this was a plea to hive off quangos to the private sector, where salaries would balloon even higher.
Reform Scotland research director Alison Payne said: "These salaries themselves may be able to be justified - that is not for us to say.
"What cannot be justified is the use of quangos to this extent.
"They are neither fully democratically accountable nor fully independent of government, so these salary awards are subject to very little transparency or accountability.
"Scotland needs to end its love affair with quangos. They should either be reintegrated into government to make ministers accountable for them, or they should be made fully independent bodies contracting with the government to provide a service, with the government accountable for ensuring high performance."
Scottish Conservative MSP Alex Johnstone said: "The Scottish Government is ultimately responsible for many of these organisations, and it's time it got to grips with the situation.
"It spends much time bemoaning low wages, yet uses every trick in the book to ensure people working at the top of the public sector are paid private sector wages."
Jenny Marra, Scottish Labour's deputy finance spokesperson, said: "At a time when budgets are falling and families are struggling to get by, we have a responsibility to ensure we get best value from all bodies who are funded by the public purse. There are concerns about a lack of accountability in some areas and this SNP government has a responsibility to ensure our money is being spent wisely."
LibDem MSP Alison McInnes said: "These figures highlight the SNP's obsession with quangos. Taxpayers will rightly question whether this is the best use of public money when budgets are tight. People want to see better services in their local communities, not countless central quangos taking up valuable resources."
A Scottish Government spokeswoman said: "Since October 2007 the number of devolved public bodies has reduced from 199 to 113, greatly exceeding the government's original target to reduce the number by 25%.
"Mergers alone have saved £78 million, between 2007 and 2012-13, and further savings will be delivered on an annual recurring basis. Pay ranges are assigned in relation to the roles and responsibilities of the position and to support recruitment and retention of staff.
"We expect all parts of the public sector to ensure their activities deliver maximum value for money and we are continuing to look for further opportunities to simplify and streamline the public-sector landscape, to reduce costs and improve the quality and efficiency of public services."