Panasevich, the son of Russian immigrants, was born in Brooklyn and grew up in Cranford, New Jersey. He began playing on a quarter-size violin that his father made for him; his devoted parents took on extra menial jobs so he could study with good teachers, according to the Globe. Panasevich later won a fellowship to study at Juilliard and in Paris with Georges Enescu.

He served in the army during World War II; his muscular physique reportedly impressed army officials so much that they initially didn't believe he was a violinist.

After the war he became assistant concertmaster of the National Symphony Orchestra in Washington, D.C., where he met Carolyn Clarke, a horn player. They married in 1947 and lived an itinerant musicians' life for a few years.

Panasevich became concertmaster of the Brevard Music Festival in North Carolina and played with the Ballet Russe de Monte Carlo before joining the BSO. In addition, he taught privately and at Boston University and the Boston Conservatory. He also was a founding member of the Cambridge String Quartet.

Panasevich was also an avid golf player; his daughter told the Globe that when the BSO played at Tanglewood he would "see how many holes he could squeeze in between open rehearsal and afternoon rehearsal."