Joseph V. Shields Jr.'s homebred Puzzlement wore down stablemate Bowman's Band in deep stretch to win the $100,000 Hal's Hope Handicap (gr. III) by a neck, giving trainer H. Allen Jerkens his third win on opening day at Gulfstream Park Saturday.Ridden by Jorge Chavez, Puzzlement completed the 1 1/16-mile Hal's Hope in 1:42 1/5. Stockholder finished third, eight lengths behind the runner-up Bowman's Band, who was a slight 2-1 favorite in the field of seven. They were followed by two lengths by Gander.Puzzlement trailed through the opening half-mile, which went in :47 2/5 as 45-1 shot Vinemesiter showed the way. After six furlongs in 1:11 2/5, Chavez angled Puzzlement to the outside on the final turn and the 5-year-old bay picked up steam down the stretch to edge ahead of Bowman's Band in the final strides. Bowman's Band opened up by 2 1/2 lengths in the stretch after stalking the lead while wide, but could not finish with the winner.Carrying 116 pounds, Puzzlement was making his first start since a third-place finish in the Woodward at Belmont Sept. 6. The Florida-bred son of Pine Bluff-Taine (by Sir Ivor) won for the sixth time in 21 career starts while pushing his career earnings to $687,590. Puzzlement's last victory came in Saratoga Breeders Cup Handicpa (gr. II) in August.Jerkens won earlier on the Gulfstream card with Hail Stormy ($5.40) in the fifth race and Buju ($4.40) in the seventh.Puzzlement paid $7.40, $3.40 and $2.40. Bowman's Band, the 118-pound high weight ridden by Ramon Dominguez, returned $3.40 and $2.60. Stockholder, Jerry Bailey aboard paid $2.40 to show. The $2 exacta was worth $21.20.