The small fossil mandible bone is 15 million to 17 million years old, about five million years older than the previously oldest-known fur seal fossil.
And it provides a ''missing link'' that helps fill in a gap of about five million years in fur seal and sea lion evolutionary history.
US-born, Mr Boessenecker (29) had been visiting California with his Otago PhD supervisor, geologist Prof Ewan Fordyce, to attend a scientific conference in 2013, and had then decided to visit a museum in Orange County.
The fossilised partial jaw, with several well-preserved teeth, had been recovered from a 15 million-17 million-year-old rock formation in Southern California in the early 1980s, but was previously misidentified as a walrus fossil.
Mr Boessenecker had been looking through several small fossils at the museum and instantly knew one 6cm-long fossil was not from the small walrus Neotherium but a tiny, early fur seal.
''I stood there with the specimen in my hand and my mouth dropped open for a few minutes.''
Finding this missing part of the fossil record was ''very exciting'' because fur seals and sea lions - the family Otariidae - had a limited fossil record that, before his discovery, extended back only to about 10 million-12 million years ago.
Previously, there had been no fossil evidence for the first five million years of fur seal and sea lion evolution, and it was ''extremely satisfying'' to have remedied that.
This unexpected discovery has just been published in the UK Royal Society journal Biology Letters.
Mr Boessenecker and co-author Morgan Churchill, a colleague from the University of Wyoming, have named this new genus and species of fur seal Eotaria crypta.
The genus name Eotaria means ''dawn sea lion''.
