C3 Inc., a Reston minicomputer products and systems firm, posted a 68 percent increase in fiscal-year profits by putting all its business eggs into one strategy basket: government contracting.

For the year ended March 31, the company said yesterday it had earnings of $8.4 million (98 cents a share) compared with its 1981 earnings of $5 million (66 cents).

Fourth-quarter profits grew 53.3 percent to $2.4 million (28 cents) from $1.6 million (18 cents) the year before.

Revenues at C3, which does 95 percent of its business with the federal government and most of that at the Defense Department, climbed 49.6 percent to $48.6 million during the fiscal year from $32 million the year before. Fourth-quarter revenues were $13.6 million, a 34.4 percent gain over the corresponding quarter's revenues of $10.1 million.

Frank J. Gaudette, vice president of finance and administration, said yesterday that, although there had been slight cutbacks in the government's defense contracting, there was nothing in the offing that would create a "major problem" for C3's earnings this year.

Essex Corp., a professional services company in Alexandria, reported a threefold growth in first-quarter profits to $146,413 (13 cents a share) from $39,856 (6 cents) last year. Revenues grew to $3.7 million from $2.7 million in the first quarter of 1981.

Company officials attributed the gains in profits to expanding business, short-term interest income and reduced interest expenses.