Private World, within inches of suffering her first defeat, fought back at the wire under jockey Kent Desormeaux to win the $100,000 Moccasin Stakes for 2-year-old fillies by a nose over 12-1 shot True Xena on Sunday at Hollywood Park.The daughter of Thunder Gulch overcame a bump by the runner-up while losing the lead inside the sixteenth pole, but she gamely battled back to post her third straight victory. The stewards reviewed the stretch run, but made no change. "It wasn't easy this time," said Desormeaux, who was aboard the chestnut filly when she won the Anoakia Stakes at Santa Anita in her last start Oct. 23. "She idled a little bit once I cleared and got a length in front. When (True Xena) got to her collar, she tried to re-engage, but I had lost a lot of momentum. She was lucky to win. She did a very good job to battle on."Private World, the 7-2 third choice in the field of seven 2-year-old fillies, paid $9.80, $5 and $3.20. True Xena, ridden by Jon Court, paid $8.80 and $4.40. Favorite Cotton Bay, another 2 1/2 lengths behind with Victor Espinoza aboard, returned $2.80. The final time for the seven-furlong event was 1:22 1/5.Private World made the lead and dueled on the inside with Bettarun Fast while running easily through solid fractions of :22: 2/5 and :45 2/5. True Xena, chasing gamely in third, took up the charge on the outside as Bettarun Fast gave way in upper stretch and the two battled through the lane."She just started getting in in the final yards," Court said of the runner-up. "She began laying in pretty severely. I worked on her left-handed, and it seemed she corrected and was going about her business. But when I went back to her right-handed, Kent's horse was coming back on. I had to take a hold of her before I annihilated Kent."Private World, owned by Thoroughbred Capital Partners and trained by Bob Hess Jr., was raised on the outfit's farm on the Utah/Idaho border before being sent to Southern California. She broke her maiden in September at Del Mar and came back to win the Anokia. Sunday's victory, worth $60,000, boosted her earnings to $141,075.