The pair, who manage the Templeton Emerging Markets Bond Fund alongside Michael Hasenstab, saw off Baillie Gifford's Japanese experts Sarah Whitley and Matthew Brett when performance figures for the three years to December 31 were compiled by financial publisher Citywire.
They headed a strong Franklin Templeton showing in the upper reaches of the table.
Peter Moeschter and Dylan Ball, managers of the Templeton Euroland, Templeton European, Templeton Global and Templeton Growth funds took seventh spot.
Heather Arnold, manager on the Franklin Templeton Global Growth and Value, Templeton Euroland, Templeton European, Templeton Global and Templeton Growth funds was in 11 place.
Ms Burakreis, who is based in San Mateo, California, and Mr Freire, who operates out of Sao Paulo, Brazil, were 17th of asset managers in 35 countries whose performance is measured by Citywire, the highest ranking among those working for investment houses with a significant presence in Scotland.
This was up from 23rd place last month and 3930th position previously.
Ms Burakreis joined Franklin Templeton in 2006 as a research analyst for its fixed income group having previously worked at the World Bank and at investment bank Salomon Brothers.
She is responsible for analysis of sovereign credits and global macroeconomic trends with a particular focus on Europe, the Middle East and Africa.
Mr Freire is Franklin Templeton's Brazilian fixed income chief investment officer. He joined the house in 2007 having been a portfolio manager for Bank Boston Asset Management.
Franklin Templeton's number of rated managers increased to 13 from 12 the previous month as Philippe Brugère-Trélat's improving performance on Franklin Mutual Euroland, Franklin Mutual European, and Franklin Mutual Global Discovery was deemed sufficient for a rating.
This put the firm joint second in numbers with Edinburgh's Standard Life Investments which lost a rating when its head of credit and aggregate Craig MacDonald was deemed to have insufficiently strong performance running its European Corporate Bond and Global Corporate Bond funds.
Baillie Gifford of Edinburgh retains the highest number of rated managers at 21.
They include Ms Whitley and Mr Brett who were unable to reclaim the top spot they occupied for five months until being pushed down to joint third position last month.
This was despite their overall ranking improving from 36th to 31st in the latest rankings.
Former table-topper Audrey Ryan, manager of the Kames Ethical Cautious Managed, Kames Ethical Equity, and Kames UK Opportunities funds secured fifth spot.
This was ahead of David Gait, manager of First State Asia Pacific Sustainability, First State Gbl Emerging Markets Sustainability, First State Indian Subcontinent and First State Worldwide Sustainability funds.