Hansgen was born in Westfield, New Jersey, the son of Frederick and Elfreda Hansgen. He began practicing on a homemade dirt track built on the family farm and purchased his first Jaguar before racing at Bridgehampton in 1951, finishing fifth on debut and taking a second-place finish at Allentown not long after. He and his father ran a Jaguar dealership, and his success with the D-Type was such that he was eventually invited to join the Briggs Cunningham team — one of the era's most prestigious American racing outfits.
His early Sebring appearances included a tenth-place finish in 1952 in an MG TD shared with Randy Pearsall. He returned to Sebring in subsequent years with Jaguar machinery, progressing through the Jaguar XK120, C-Type, and eventually D-Type.
Hansgen became SCCA National Champion in 1956 driving a Jaguar D-Type, and then repeated the title in 1957, 1958, and 1959 — four consecutive championships. In 1957 he contested the inaugural race at Virginia International Raceway, qualifying on pole in his D-Type but finishing second behind Carroll Shelby. When the Cunningham Jaguars returned to VIR later that year, Hansgen won the featured President's Cup Race in dramatic fashion: he started 16th, survived a rain-shortout pit stop that dropped him two laps behind the field, then set a record-setting pace to catch and pass the leaders for the win. The New York Times named him "Best Driver of the Year" and Sports Illustrated nominated him "U.S. Sports Car Driver of the Year" for 1957. That season he also won at Lime Rock, Road America, Marlboro, Montgomery, Thompson, Watkins Glen, and Bridgehampton.
In 1958 he raced Lister-Jaguar machinery in the UK, winning at Snetterton, then campaigned the car in the United States with victories at Marlboro, Virginia, Cumberland, Bridgehampton, Lime Rock, and Road America. He took his fourth SCCA title in 1959 at the wheel of the same Lister-Jaguar.
Also in December 1959, Hansgen won the Formula Junior race at the inaugural United States Grand Prix meeting at Sebring, driving a Stanguellini.
Hansgen drove Cunningham's Tipo 61 Maserati Birdcage to seven SCCA National wins across 1960–1961. At Le Mans in 1960 he partnered Dan Gurney in a Jaguar E2A, retiring after 89 laps; in 1961 he shared the rear-engined Maserati Tipo 63 with Bruce McLaren, again retiring early. His 1962 Le Mans entry with McLaren in the Maserati Tipo 151 Coupé completed 177 laps before retiring. He and Augie Pabst drove a Jaguar E-Type Lightweight at the 1963 Le Mans, retiring after just 8 laps.
In 1961 the Cunningham Tipo 63 proved troublesome in development, but Hansgen took the car's only wins at SCCA Nationals at Bridgehampton and the Elkhart Lake 500 (co-driven with Augie Pabst).
When Cunningham withdrew from racing at the end of 1963, Hansgen moved to John Mecom's team.
Hansgen made his Formula One World Championship debut at the 1961 United States Grand Prix at Watkins Glen on October 8, 1961, aged 41, driving a Cooper T53-Climax entered by Momo Corporation. He qualified fourteenth but retired after 14 laps following an accident. In October 1964, Colin Chapman hired him to drive the third Lotus 33-Climax works car at the United States Grand Prix at Watkins Glen. He finished a solid fifth place, scoring two championship points and finishing 16th in the final standings. His Formula One record totalled two entries, one classified finish, and two career points.
Hansgen qualified for the 1964 Indianapolis 500 in the MG Liquid Suspension Special — a Huffaker-built Offenhauser-powered car entered by Kjell Qvale — starting from tenth on the grid and finishing thirteenth. At 44 years old he was the fastest rookie qualifier and, at that age, the oldest rookie to qualify for the race up to that point, a record he held for 28 years until Lyn St. James qualified in 1992 aged 45. In 1965 he returned in the same MG-Huffaker-Offenhauser, starting twenty-first and finishing fourteenth.
With Mecom Racing, Hansgen drove a range of machinery including a Ferrari 250LM, a Lola T70, a Lotus 19, and a Scarab Chevrolet. In September 1964 he and Augie Pabst took victory in the US Road Racing Championship race at Road America in Mecom's Ferrari 250LM. He won the Bridgehampton Double 400 Km in 1964 in a Scarab-Chevrolet, earning his longstanding nickname "King of the Bridge."
In 1965 he won the Monterey Grand Prix at Laguna Seca Raceway on October 17 driving John Mecom's Lola T70-Ford.
It was during this period that Hansgen became a mentor to a young Mark Donohue. He promoted Donohue to make his Sebring debut in Mecom's Ferrari 250LM; the pair finished second in class and eleventh overall. In Donohue's autobiography The Unfair Advantage, he credited Hansgen with his biggest break in racing, and Hansgen is also noted for later introducing Donohue to Roger Penske.
For 1966 Hansgen joined Holman and Moody as lead driver for their Ford GT40 Mk2 in the World Sportscar Championship, insisting on Mark Donohue as co-driver. The pairing finished third at the 24 Hours of Daytona and second at the 12 Hours of Sebring, behind the winning Ford of Ken Miles and Lloyd Ruby.
Hansgen then travelled to France for the Essais Préliminaires — the preliminary test sessions ahead of the 1966 24 Hours of Le Mans. On the morning of April 2, 1966, practicing on a wet track, he lost control of the 7-litre Holman and Moody Ford GT40 Mk2. He drove onto an escape road but was unaware that a barrier had been erected across it for spectator safety. He crashed heavily and was taken first to a local hospital, then to the United States Army Hospital in Orléans. Team manager Carroll Smith had warned him to moderate his pace in the damp conditions, and a Ford spokesman stated the car appeared to have been aquaplaning. Hansgen remained unconscious and in critical condition for five days, dying on April 7, 1966, at the age of 46.
He was survived by his wife Beatrice and their two children, Beverly and Rusty. He was buried in the New Germantown Cemetery in Oldwick, New Jersey.
Hansgen's career bridged the amateur roots of post-war American road racing and the professional era that followed. His four straight SCCA titles, his endurance racing campaigns with Cunningham, his late-career Indianapolis appearances, and his brief but competitive Formula One outings marked him as one of the most versatile American drivers of his generation. His most enduring legacy may be the role he played in launching Mark Donohue's career — a mentorship that shaped one of the most important figures in subsequent American racing history.