Kvapil grew up working on cars in his father's garage in Wisconsin. He began racing in 1992 at age sixteen at Rockford Speedway in the NASCAR Weekly Racing Series, winning the American Short Tracker division track championship there in 1994. In 1995 he moved to super late models at Madison International Speedway, was named Rookie of the Year, and became the track's Late Model champion in 1996 — the youngest driver to win that title. He subsequently competed in the ARTGO Series, a Midwest asphalt touring series, finishing in the top ten in points from 1998 through 2000.
Kvapil debuted in the Craftsman Truck Series in 2001 with Addington Racing, winning his first race in just his 21st start at Texas Motor Speedway. He finished fourth in points and was named Craftsman Truck Series Rookie of the Year. In 2002 he added a second win at Memphis Motorsports Park.
A funding shortage at Addington prompted Kvapil to move to Xpress Motorsports for 2003. He won one race at Bristol Motor Speedway and delivered an extraordinary season of consistency: 22 top-tens in 25 races — an 88 percent rate — and a 99.9 percent lap-completion figure, missing just one lap all season. He clinched the 2003 Craftsman Truck Series championship at the season finale at Homestead-Miami Speedway after both closest rivals, Brendan Gaughan and Ted Musgrave, encountered race-day trouble.
In 2004 Kvapil moved to a Toyota programme for Alexander Meshkin's Bang! Racing team, winning at Michigan International Speedway — giving Toyota their first win in NASCAR's top-tier divisions — and again at New Hampshire International Speedway. He finished eighth in points.
Kvapil joined the Cup Series full-time in 2005 with Penske Racing in the No. 77, replacing Brendan Gaughan. He scored two top-tens in his debut Cup season, finishing seventh at Bristol and again at Phoenix, ending the year 33rd in points. When Kodak withdrew sponsorship after the season, the No. 77 programme was suspended.
For 2006, Kvapil moved to PPI Motorsports in the No. 32 Tide Chevrolet, finishing 36th in points. When PPI closed after the season, Jack Roush recruited Kvapil back to the Truck Series for 2007 in the No. 6 Ford, where he posted four wins and twelve top-tens. Roush then facilitated a return to Cup via Yates Racing in 2008 in the No. 28 Ford. Despite chronic sponsorship difficulties, Kvapil recorded four top-ten finishes that year including a sixth at Talladega — his career-best Cup finish — and won the pole at the fall Talladega race, the last pole Yates Racing would ever claim. He finished 23rd in points.
The Yates operation closed after six races into 2009 due to funding failure. Kvapil spent portions of 2009 qualifying cars for other drivers and joined Front Row Motorsports for 2010 and 2011 in the No. 38, rotating among car numbers to maintain points position. He was released from FRM at the end of 2011.
Kvapil drove for BK Racing in 2012, recording his second-best Cup points finish of 27th, and for BK Racing again in 2013, where nine DNFs — five due to engine failures — dropped him to 31st in points. BK released him before the 2014 season.
In 2014 Kvapil ran part-time in both the Cup and Truck series. A memorable qualifying attempt for the 2015 Cup season at Atlanta was abandoned when his car, hauler, and truck were stolen from a hotel parking lot. He spent 2015 through 2017 primarily in the Truck Series with MAKE Motorsports (later Beaver Motorsports), scoring a fifth at the 2016 Daytona opener. He made just one Truck start in 2019, at Martinsville, which marked his last NASCAR appearance.
Kvapil's legacy rests primarily on his 2003 Craftsman Truck Series championship, achieved through relentless consistency rather than raw win count. His ability to deliver a 99.9 percent lap-completion rate in a championship season reflects disciplined, measured racing. His transition to the Cup Series illustrated the financial fragility facing underfunded teams, as sponsorship collapses cut short what might otherwise have been a longer top-series career. His contribution to Toyota's first NASCAR upper-tier victory in 2004 also holds historical significance.