The privately owned Stirling company, which designs and supplies electrical systems for use in hazardous areas on oil rigs, saw turnover rise 11.5% from £36.6 million to £40.8 m in the 12 months to May 31 this year.
UK turnover grew from £34.6m to £37.9m with other European sales dropping from £1.26m to less than £458,000.
However, turnover generated in the rest of the world soared 222% from £744,227 to more than £2.4m.
Accounts filed at Companies House show pre-tax profits increased from £1.04m to a record of almost £2.2m in the same period.
Writing in the accounts, managing director Colin Rowley said: "Dron & Dickson benefited from strong levels of activity in the oil and gas sector.
Continued growth delivered record results and turnover, profit and net assets all increased."
While more than 90% of business is generated in the UK, Mr Rowley highlighted that there was 44% growth in overseas sales.
The Dron & Dickson JLT subsidiary in Dubai completed its first year of trading and also acquired Abu Dhabi-based Totus Energy Electromechanical Contracting for more than £206,000. Separately Dron & Dickson Brasil was set up in February this year.
Mr Rowley said those operations, along with the UK business, will "form the nucleus" of Dron & Dickson going forward.
The directors said among the risks and uncertainties facing the business were the North Sea tax regime, changes to the long term oil price and the availability of skilled workers.
However the UK oil and gas sector was described as "robust in the medium term" particularly as Dron & Dickson's products focus on asset integrity and maintenance.
The company's net debt was shaved from £1.95m to just short of £348,000.
Average staff numbers went from 140 to 182 with the accounts showing the business now has in excess of 100 people working offshore.Employee costs rose from £8m to more than £9.1m, with directors' emoluments going from £215,379 to £234,776.
The highest paid director received £85,068, up from £69,724.
There were £363,828 of equity dividends paid, against £203,065 in the previous year.
Dron & Dickson began life as a supplier of explosives to the mining and quarrying industries in 1927 before moving into oil and gas market in the 1970s.
Mr Rowley led a management buy-out of the firm from his father Arthur in 2007, supported by directors Colin Maver and Gerry Lafferty.