Saarinen was born and raised in Turku, in south-west Finland. At the age of 15 he worked as an apprentice and test rider for Tunturi-Puch, a motorcycle factory in Turku that assembled mopeds and motorcycles under licence from the Austrian Puch manufacturer. He made his racing debut in an ice race at Ylone in 1961, finishing second, and competed in ice racing, grasstrack racing, and road racing alongside his close friend Teuvo Lansivuori.
By 1965 Saarinen had won the 250cc Finnish ice racing national championship. He made his Grand Prix debut on 4 August 1968 at Imatra, riding a 125cc Puch to eleventh place in the Finnish Grand Prix, lapped three times by world champions Phil Read and Bill Ivy. In 1969 he won both the 125cc and 250cc Finnish motorcycle road racing national championships, acting as his own mechanic throughout.
Saarinen competed in his first full Grand Prix season in 1970, financing his racing career by convincing three bank managers to fund him under the mistaken belief they were supporting his education. He finished the 250cc season in fourth place despite missing the final three rounds to complete his engineering degree at the Turku Technical Institute.
In 1971 he served notice of his ability by winning the 350cc Nations Grand Prix in Italy and finishing second in the class standings behind Giacomo Agostini. He also placed third in the 250cc World Championship. His distinctive riding style — keeping his chest low above the fuel tank and sliding the rear tyre through corners with his knee extended — drew notice from Kenny Roberts when the American witnessed him race at Ontario Motor Speedway in 1972.
Saarinen received factory Yamaha support for the 1972 season, riding the YZ634 in the 350cc class and a production 250cc Yamaha supplied by the Finnish importer. After an inconsistent start to the 250cc championship, Yamaha assigned him the factory YZ635 machine previously allocated to Barry Sheene, and Saarinen responded by winning four of the last six races to clinch the 250cc World Championship ahead of Renzo Pasolini and Rod Gould. He also finished second in the 350cc class, beating Agostini at the Nurburgring — Agostini's first head-to-head defeat since 1967. After the world championship season ended, Saarinen won nine consecutive races during a British tour, including the Race of the Year at Mallory Park.
For 1973 Yamaha contracted Saarinen as their top rider in both the 250cc and 500cc classes aboard the newly developed YZR250 and the four-cylinder two-stroke YZR500 0W20, representing Yamaha's first serious challenge to MV Agusta's sixteen-year dominance of the 500cc class.
Saarinen began the year by winning the Daytona 200 on a smaller 350cc Yamaha against factory 750cc rivals from Kawasaki and Suzuki, becoming the first European rider to win that event. He then opened the Grand Prix season with double victories at both the French and Austrian Grands Prix, winning the French 500cc race more than 16 seconds clear of Read while Agostini crashed. Heading to the Nations Grand Prix at Monza he led both the 250cc and 500cc championships.
On the first lap of the 250cc race at Monza, second-placed Renzo Pasolini's motorcycle lurched sideways and crashed into a steel guardrail, killing him instantly. Pasolini's machine bounced back onto the circuit and struck Saarinen, knocking off his helmet; Saarinen was then hit by another motorcycle and sustained fatal injuries. More than 14 riders were involved in the chain-reaction crash. The official inquiry, issued in September 1973, attributed the accident to engine seizure in Pasolini's motorcycle, though controversy persisted for years over whether an oil slick left by a 350cc machine during the preceding race contributed.
The deaths of Saarinen and Pasolini at Monza in 1973 galvanised motorcycle racing's safety movement. Factory teams from Suzuki, MV Agusta, Harley-Davidson, and Yamaha joined to demand improved circuit conditions; Yamaha withdrew from the remainder of the 1973 season to honour Saarinen's memory. Riders boycotted several subsequent Grands Prix over safety concerns, tensions that culminated in 1979 when Kenny Roberts and journalist Barry Coleman attempted to launch a rival World Series championship. The resulting FIM reforms substantially increased prize money and imposed stricter safety regulations on race organisers, leading to the removal of dangerous circuits from the calendar and the replacement of steel guardrails with run-off areas.
Streets named after Saarinen exist in Turku and in Pesaro, Italy, outside the Benelli factory. The name Jarno became widely popular in Italy following his death. He was inducted into the FIM MotoGP Hall of Fame in 2009. Saarinen won 15 Grands Prix during his career and was six times Finnish road racing national champion.