Park is the youngest of four sons and grew up on Long Island, New York. He began his career not at an entry level but directly in NASCAR Modifieds, racing on Long Island for longtime National Modified Championship contender Bob Park. After establishing himself in weekly Modified competition at Riverhead Raceway, he advanced to the Featherlite Modified Series, where he won multiple races and became a championship contender. This success brought him to the attention of Dale Earnhardt, whose phone messages Park initially ignored, believing friends were pranking him.
Earnhardt hired Park in 1996 for a single Busch Series start in Charlotte, resulting in a 29th-place finish. For the full 1997 Busch season, Park drove Earnhardt's No. 3 AC-Delco–sponsored Chevrolet, winning three races at Nashville, Michigan, and Richmond and finishing third in the Busch points standings while claiming Rookie of the Year honors.
Park moved to Dale Earnhardt Inc.'s Winston Cup program in 1997, attempting eight Cup races and qualifying for four of them in the No. 14 car. He also made one start for Felix Sabates at Martinsville. In 1998 he switched to the No. 1 Chevrolet for DEI; during practice at Atlanta Motor Speedway a tire failure caused three successive hard impacts that left him with a broken leg, broken collarbone, broken shoulder blade, and two chipped teeth. He recovered and returned to the car later that season. In 1999, his first near-full Cup campaign, Park finished 30 of 34 races and recorded a best result of sixth in the Kmart 400 at Michigan, finishing 14th in points.
The 2000 season was Park's statistical high point. He recorded a career-best six top-fives and thirteen top-tens, and took his first Cup victory at his home circuit of Watkins Glen International, winning the Global Crossing @ The Glen. He finished 11th in points.
In 2001, Park was involved in a multi-car crash at lap 173 of the Daytona 500; he was unhurt, but the race was overshadowed by the fatal crash of his team owner Dale Earnhardt on the final lap. The following week, Park won the Dura Lube 400 at North Carolina Speedway in an emotionally charged victory for the grieving DEI team. He recorded three runner-up finishes during the season, at Darlington, Texas, and Dover, and sat as high as fourth in points before fading to 13th. That September, racing in a Busch Series event at Darlington, his steering wheel came off while under caution and he was struck on the driver's side by Larry Foyt accelerating for the restart; the injuries Park sustained effectively curtailed his competitive momentum for the rest of his career.
Park returned in 2002 but struggled with on-track incidents including a spectacular flip at Pocono Raceway after contact with Rusty Wallace and a collision with teammate Dale Earnhardt Jr. He finished 33rd in points. His early 2003 form was similarly poor, and DEI released him midseason in an effective swap with Richard Childress Racing, Park taking over the No. 30 car while Jeff Green moved to the No. 1. His best RCR result was a fifth-place finish at Michigan International Speedway.
Park joined Las Vegas–based Orleans Racing in the Craftsman Truck Series in 2004, driving the No. 62 truck. Despite not winning, he finished ninth in points and was voted Most Popular Driver by his peers. In 2005, he won the American Racing Wheels 200 at California Speedway to become one of a small number of drivers to have won in all three of NASCAR's premier national series. Park and Orleans Racing parted ways that October when Dodge withdrew financial support from many truck programs.
Park returned to the NASCAR Camping World East Series in 2008 and 2009, finishing ninth and fifth in points respectively and winning the Edge Hotel 150 at Adirondack International Speedway in August 2009. He made a brief Sprint Cup return in July 2010 with Tommy Baldwin Racing at Daytona, starting 39th and finishing 13th while leading one lap in a fan-sponsored tribute car honoring nine-time NASCAR Modified champion Richie Evans.
In January 2013, Park won a Whelen Modified Tour race at Daytona — his first modified win since 1996 — after being pushed from behind into the lead on the final lap in contentious circumstances.
Park and Mariah Carey became acquainted in high school through mutual friends, as both grew up in the same Long Island area. Park was inducted into the Suffolk Sports Hall of Fame in the Auto Racing category with the Class of 2004. He previously owned and operated a Batteries Plus Bulbs franchise in Mooresville, North Carolina, which he sold in September 2022.