It was also the first time a Dodgers player had hit for the cycle at Dodger Stadium and just the ninth time a Dodgers player had ever accomplished the feat.
And Parker's cycle came on a 10th-inning triple, so Hudson was the first Dodgers player to accomplish it in a nine-inning game since Gil Hodges did it on June 25, 1949.
Parker, who was a Gold Glove winner and switch-hitter like Hudson, offered his congratulations to Hudson with a statement after the game.
"A lot has happened in baseball and the world over the last 39 years," Parker said. "Cesar Izturis and Gary Sheffield came closest to hitting for the cycle. I've had a lot of fun with it. A lot of friends become aware of it over the years and now people realize how difficult it is to accomplish.
"Congratulations to Orlando. I hope he appreciates he's in a very unique club. I can't believe only two people in 51 years. It's great fun to have a game like that. He'll be on a high for two weeks."
It was also just the second time a cycle happened at the stadium as the Angels' Jim Fregosi hit for the cycle against the Yankees on July 28, 1964. But the stadium was referred to as Chavez Ravine when the Angels played home games there until 1966, so this was technically the first at "Dodger Stadium."
Hudson, with his wife, two children and parents in attendance for the game, had his first hit of the day on an infield single in the first inning against Giants left-hander Randy Johnson. He then followed up with a solo home run in the third and a double against Johnson in the fourth.
Hudson completed the cycle with a triple down the right-field line against Giants reliever Brandon Medders.
But he admitted after the game that he didn't even know he had hit for the cycle until teammates told him when he reached the dugout after scoring on James Loney's single. Pitching coach Rick Honeycutt, Casey Blake and Doug Mientkiewicz were the first tell him.
"I was like, 'Congratulations for what?'" Hudson said. "I had no idea what was going on. And then I realized it was the cycle. I was wondering why they were cheering for me like that."
Hudson was also proud because his cycle came mostly against Johnson, who is just five wins away from 300 career victories.
"Facing Randy is already tough," Hudson said of his former teammate. "I've faced Randy quite few times and he did a number on me. But I guess I kind of reversed that today. I have a lot of respect for Randy. He's a first-ballot Hall of Famer."
Hudson struck out in his last at-bat in the seventh inning and finished 4-for-5 with three runs scored and two RBIs.
Hudson simply stole the show for the Dodgers as his cycle overshadowed a dominating 11-strikeout performance by Chad Billingsley and two home runs by Andre Ethier in the Dodgers' 11-1 win.
But after setting the bar so high, Hudson said that he hopes that Dodgers fans don't expect a similar performance from him every home game this season.
"Dodger fans can't expect this every day," he said. "It's a hard enough game as it is. But I'm going to go out there and give it 110 percent every game. And I'll have the same smile on my face if I'm 0-for-4 or 4-for-4."