The trainer and jockey won the Juvenile Turf with Modern Games on Friday and the Mile with Space Blues earlier on Saturday's card.
Aidan O'Brien's Broome, ridden by Irad Ortiz, looked to have put the race to bed with a decisive move turning into the short home straight, taking a couple of lengths out of the field.
Yibir had been settled at the rear by William Buick, who along with last year's winner Tarnawa, had a posse of horses in front of him with just two furlongs to run.
But once Buick pulled the Great Voltiguer winner out into the home straight, Yibir hit his full stride and ran down Broome comfortably in the end.
Roger Varian's Teona was not far back in third, with O'Brien's Japan in fourth. Tarnawa found little in the finish and was well beaten.
Buick said: "Once I turned halfway down the back straight, I was in a better position. I followed Tarnawa but she was never going as well as I thought she would.
"It was the one race I didn't know how to assess. Yibir is a complex character, as you saw last time he ran over here, I was just hoping he saved a bit for the finish.
"Halfway round the turn I could see Broome had gone, but my horse picked up in a way you rarely see. It was a great performance from a young, up and coming horse."
Appleby said: "As you've seen he's run some quite indifferent races this season, like at Goodwood, but then he ran well at York.
"The key was getting him to settle and Jamie Spencer did that at Belmont.
"It was a hard ride for William, he was taking him on but it all worked out."
As well as saddling three winners, Appleby also had two withdrawn at the start over the course of the meeting and said: "It's been a fantastic weekend, I can even take a couple home fresh!
"There were lots of emotions (on Friday) and I felt sorry for the crowd that winning tickets didn't come off.
"I knew the right horse was left in the gate in Space Blues and Yibir was the icing on the cake - he's been galloping with all our best middle-distance three-year-olds.
"Next year this horse brings experience to the table in middle-distance races. We won't be taking anything to Hong Kong, they will all have well-earned vacations."
O'Brien said of his three runners: "Broome ran a great race and we thought he was in good form. He was just a bit lazy in front, while Ryan (Moore on Japan) got chopped and Frankie (Dettori) said Bolshoi Ballet was too babyish."
Varian was pleased with Teona's effort and said: "David gave her a great ride.
"It's not an ideal track for her, but she ran a race of real credit. She's a lengthener and we had to angle out, and didn't have the acceleration to put the race to bed."
Tarnawa was last seen when narrowly beaten in the Prix de l'Arc de Triomphe at ParisLongchamp last month, going down by just three-quarters of a length in testing conditions.
Jockey Colin Keane felt that French outing may have left its mark as the mare came home 11th.
He said: "She ran flat. I think France last time on very soft ground took plenty out of her. She seemed fine after the race."