Ms Burakreis, who is based in San Mateo, California, and Mr Freire, who operates out of Sao Paulo, Brazil, were ranked top when performance figures for the three years to November 30 were compiled by financial publisher Citywire.
This put an end to the five-month reign of Baillie Gifford's Japan specialists Sarah Whitley and Matthew Brett. They now sit in joint third position.
The Franklin Templeton pair, who run the Templeton Emerging Markets Bond Fund, were 23rd of asset managers in 35 countries whose performance is measured by Citywire, the highest ranking among those working for invest-ment houses with a signif-icant presence in Scotland. This was a jump from their previous position at 3930.
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 has 240 staff in Edinburgh after setting up shop in the capital in 1988. Among their number is Dylan Ball, who shared sixth spot in the Scottish table with Canadian colleague Peter Moeschter. The pair run the Templeton Growth fund.
Lesley Duncan, manager of the Standard Life Investments UK Ethical Fund, secured fifth spot.
The Herald-Citywire survey measures risk-adjusted performance against relevant bench-marks. About 100 fund managers working for investment houses with a significant presence in Scotland qualify for a Citywire rating, which denotes strong performance.
Of these fund managers, 21 are with Baillie Gifford, 14 are with Standard Life Investments. Franklin Templeton has 12 managers with a Citywire rating, up from nine the previous month. This allowed it to leapfrog Artemis which went from nine to 10 rated managers.