After dropping the weakest score from their total, the Saudi team are carrying just one fault into Monday's second round.
"I cannot describe my feelings I am so happy," Prince Abdullah al Saud told reporters.
Prince Abdullah is the second royal Olympian to have made an appearance in the Greenwich Park arena. Zara Phillips, granddaughter of Queen Elizabeth and daughter of Princess Anne, was part of the British team that won silver in eventing.
Britain, Sweden, the Netherlands and Switzerland were tied with a first-round score of four faults. Faults earned over the two days are added together to determine the team winner.
Canada, who won team Olympic silver in 2008, were close behind at five faults but suffered a serious blow to their prospects when rider Tiffany Foster was disqualified. This left only three members in contention.
All other four-member teams have the option of dropping their weakest score at the end of the two days but all scores will count for Canada.
Foster was disqualified after one of horse Victor's forelegs was found to be hypersensitive by the veterinary team.
Veterinarians measure limb heat to determine sensitivity under rules set up in 2005 by the International Federation for Equestrian Sports (FEI) to keep riders from purposely sensitising their horse's legs to make them jump more carefully.
"There is no accusation of malpractice, but the horse has been deemed unfit to compete by the Ground Jury," the FEI said in a statement.
The FEI stresses that horses' legs can become hot because of injury or infection.
"I am sick about it," said Ian Millar, who at 65 is making a record 10th Olympic appearance and who offered his team some consolation by jumping a perfect round.
"Having said that, we did it before in Beijing and we got it done, but it's doing it the hard way for sure. And, as I say, our team, all the riders are devastated by this situation."
The Canadians protested the decision but their appeal was denied by the FEI.
Brazil and defending Olympic team champions the United States squeaked into the top eight to qualify for round two while Germany, France and Belgium surprised by being among those that failed to make the cut.
Since Monday's round also serves as a third qualifier for the individual competition, leading individuals will jump on Tuesday, regardless of whether their teams are in the running.
All riders who finish in 35th position or above, including ties, after Monday will go through to the two-round individual contest on Aug. 8.
They will go into the individual final with a clean slate since their qualifying scores are not carried forward.
Prince Abdullah was tied for first in the individual rankings with 11 other riders, including hot gold medal prospects Nick Skelton from Britain and American Rich Fellers.
"I feel great," said Skelton after jumping an effortless clear round on Big Star. "He's in great condition. He hasn't a negative, that horse. He is the most perfect horse, all round."
For Prince Abdullah and horse Davos, the London-themed jumps were a highlight. "What with the weather, the London bus and the Tower Bridge, I felt like I was sight-seeing today," he said.
It was a second Olympic appearance for the grandson of King Abdullah and the son of Prince Miteb bin Abdullah, head of the elite Saudi Arabian National Guard.
"The equestrian national team ... achieved very positive results today in the teams competitions and we are proud. There is one more round left tomorrow. We wish them the best," said Saudi Olympic Committee general secretary, Rashed Al-Heraiwel.
Brazil and the United States have eight faults each. Fellers jumped clean but his team mates were not so lucky.
Youngest Olympic equestrian Reed Kessler had two fences down for a total of eight faults while Beezie Madden and McLain Ward each had one down to stand on a total of four faults each.