Tommy Smith, a brazen jockey who guided the bay thoroughbred Jay Trump to victory in the British Grand National in 1965 — the first time an American horse and rider won the prestigious steeplechase — died Tuesday at his home in Upperco, Md. He was 75.

He had complications from a 2001 riding accident that left him quadriplegic, said his daughter, Alexandra Smith.

Descended from a family of fox hunters, Mr. Smith was on horseback before he could walk. He grew up in the saddle, galloping after hounds through the forests, creeks and pastures of the Virginia countryside from the time his legs were long enough to reach the stirrups.

Mr. Smith would become one of the most celebrated horsemen of his generation. His accomplishments were inextricably linked to Jay Trump, the muscular gelding whose racing career almost ended before it began: The horse was nearly put down after suffering a catastrophic wound to his foreleg during a training accident as a 2-year-old.

Their Grand National victory at the historic Aintree Racecourse garnered headlines around the world and made the front pages of The Washington Post and the New York Times.

They were unlikely champions — Mr. Smith was an amateur, and Jay Trump’s odds were 100 to 6 — which made their success more remarkable, considering that simply finishing the Grand National is not guaranteed.

Since its inception in 1839, the Grand National has been regarded as the the most difficult and most dangerous steeplechase. The course of four miles, 856 yards has 30 spruce-covered obstacles, most taller than the jockeys who ride over them. Injuries of jockeys are common; so, too, are deaths of horses that break legs hurdling the timber.

A field of 47 started the race on March 27, 1965. Only 14 crossed the finish line.

Mr. Smith and Jay Trump were slow to get going. The crowd favorites, Freddie and the Rip, the latter owned by the Queen Mother, stayed toward the front for most of the race. Mr. Smith and Jay Trump wended around the course littered with fallen jockeys and riderless thoroughbreds.

“A horse fell in front of me at the third fence,” Mr. Smith told Sports Illustrated in 1965. “My horse stepped on the rider. It almost made me sick. I’ve never been in so much bedlam.”

Mr. Smith had spent the weeks before the Grand National studying videos of past races. He had walked the course and analyzed each jump for the best takeoff and landing spots. According to Sports Illustrated, Mr. Smith had found that the last jump was softer than the others.

Near the finish, Mr. Smith and Jay Trump engaged in a thrilling neck-and-neck duel with Freddie and jockey Pat McCarron.

Coming toward the last fence, Mr. Smith gambled and pushed Jay Trump to leave from a more shallow angle. The horse’s legs and belly scraped the brush but gained precious seconds turning for home. In the final 500 yards, Mr. Smith and Jay Trump edged McCarron and Freddie by less than a second.

“No runner had ever gone toward the big race with more total dedication from its rider,” author and champion jockey Dick Francis wrote in the foreword to “The Will to Win,” a 1966 book by Jane McClary chronicling Mr. Smith’s triumph. “Tommy Smith literally devoted his whole self, his will, his energy, and his body, to one end.”

Crompton Smith Jr. was born Oct. 16, 1937, in Middleburg. His father and grandfather were renowned horsemen, and he grew up steeped in steeplechasing lore. Before he was a year old, his parents strapped him into a basket on top of a pony. He took up point-to-point racing as a teenager.

He graduated from the private Taft School in Watertown, Conn., and attended Princeton University until deciding to pursue a career as a jockey.

He found Jay Trump in Charles Town, W.Va., in 1960 and arranged his purchase for $2,000.

As a green horse, Jay Trump had skittered off the track during a training exercise and gashed his leg. A veterinarian sewed the bone-deep gash with 29 stitches, saving Jay Trump from being destroyed. Despite the injury, and his winless record racing on the flat, Mr. Smith helped turn him into a champion hurdler. Together, the pair won the prestigious Maryland Hunt Cup three times, in 1963, 1964 and 1966.

Mr. Smith retired from racing in 1966 and became an executive for health-care businesses in Minnesota and Boston. He retired in 1995 and moved to Upperco in Baltimore County, where he started training thoroughbreds. In 2001, a horse he was riding tripped and Mr. Smith fell, leaving him a quadriplegic.

Survivors include his wife of 49 years, Frances Cochran Smith of Upperco; two children, William Smith of Carlisle, Mass., and Alexandra Smith of Upperco; a sister, Kitty Smith of Delaplane, in Fauquier County; and two grandchildren.

Mr. Smith said that a dose of fear was crucial for a jump jockey facing the obstacles at the Grand National.

“The adrenaline gives you that extra, sharper reflexes and makes you see and feel and heightens awareness so that everything you are goes into the race itself,” Mr. Smith was quoted as saying in “The Will to Win.” “I never knew a rider that was any good who wasn’t a little bit afraid.”