The 600-kilogramme (1,320-pound) bull named Brevito lagged behind the pack just before entering the city's bull ring at the end of a rain-slicked bull run in the annual San Fermin festival.
The straggling animal skewered 32-year-old Chicago-based journalist and author Bill Hillman in the right thigh and a 35-year-old Spanish man in the chest before being guided to the end of the bull-run.
Both men were in serious condition in hospital but their injuries were not life-threatening, regional health authorities said.
Another three runners were taken to hospital with bruises to the head and legs after they tripped over each other while racing ahead of the six fighting bulls and six steers, the authorities said.
They identified Hillman only by his initials B.H. But British journalist Alexander Fiske-Harrison, author of a book on Spanish bullfighting who has fought bulls in the ring, said the victim was his friend Bill Hillman, taking part in the festival for the 10th straight year.
Missed an artery
Hillman had undergone surgery "but seemed okay, indeed happy given the amount of pain killers he was on," Fiske-Harrison wrote, explaining that the animal's horn pierced Hillman's right thigh but missed the artery.
Hillman co-authored an e-book titled "Fiesta: How to Survive the Bulls of Pamplona" along with Fiske-Harrison and several other bull running veterans.
Contributors to the book, published last month, included John Hemingway, the grandson of Ernest Hemingway whose 1926 novel "The Sun Also Rises" made the fiesta famous worldwide.
Emergency services workers erected red sheets around the other goring victim, a Spaniard who took a horn in the chest, as they applied first aid.
At one point during the run, the fighting bull charged a man who had fallen and cowered by a wooden fence. Another runner tried to coax the sharp-horned fighting bull away by pulling on its tail.
A divided pack of bulls presents one of the greatest dangers in the bull-runs that are the centrepiece of this centuries-old festival, leaving the huge animals disoriented and irritated by crowds of thousands of adrenaline-charged — and often alcohol-fuelled — thrill seekers.
Dozens more runners were treated at the scene for scrapes and bruises suffered in falls along the winding, 848.6-metre (more than half a mile) bull-run course through narrow streets that were slippery due to overnight rain.
"I saw a lot of people fall along the way," said Juan Pedro Lecuona, a 41-year-old father of four who has run with the bulls in Pamplona every year since 1989 and who was gored in the leg at a run in 2010.
The fighting bulls from the Victoriano del Rio ranch took three minutes and 23 seconds to cover the 850-metre (2,800-foot) course from a holding pen to Pamplona's bull ring, the longest time of the three bull-runs held so far this year.
Two bulls broke away from the rest of the pack at the start of the route and raced ahead but the bull that straggled behind stretched the total time of the run.
The bulls will face matadors and death in the afternoon in the bull ring.
The San Fermin festival, a heady nine-day mix of partying and adrenaline-chasing, draws hundreds of thousands of people from around the world to Pamplona, a city of around 300,000.
Fifteen people have been killed in the bull-runs since records began in 1911. The most recent death occurred five years ago when a Spanish man was gored.