Murphy became involved in motorsport by the age of eight. He progressed through karting and saloon cars before moving to Australia in his early racing years. His open-wheel credentials included winning the 1994 New Zealand Grand Prix at Manfeild in a Reynard 90D and a second-place finish in the GT2 class at the 1996 24 Hours of Le Mans, demonstrating a range beyond domestic touring cars.
He first competed at the Bathurst circuit in 1994. Over the following two seasons he drove for Brad Jones Racing in the Australian Super Touring Championship and joined the Holden Racing Team for endurance events. In 1996 he partnered Craig Lowndes to win both the Sandown 500 and the Bathurst 1000 for HRT, his first Bathurst victory. He drove for the team full-time in 1997, placing fourth in the Australian Touring Car Championship, before returning to an endurance-only role in 1998 as Craig Lowndes came back from overseas.
Murphy joined Gibson Motorsport for 1999 and 2000, finishing sixth in points in both seasons. Partnering Steven Richards, he won the 1999 Bathurst 1000. In 2001 he was part of the newly formed Kmart Racing team, an outfit built largely from the remnants of Gibson Motorsport after it switched to Ford.
The most celebrated individual achievement of Murphy's career came at the 2003 Bathurst 1000 Top 10 Shootout, when he set a lap time of 2:06.8594 around the 6.213 km Mount Panorama circuit. The time stood as the outright lap record at the circuit for seven years, eclipsed only in 2010 by Craig Lowndes. It was quickly dubbed "The Lap of the Gods" and became one of the most replayed moments in Australian motorsport broadcasting history. Murphy also won the race itself that year, partnering Rick Kelly for Kmart Racing. He won the Bathurst 1000 again in 2004, again with Rick Kelly, making him a four-time winner.
Murphy secured four home-circuit victories at Pukekohe, near Auckland, in 2001, 2002, 2003 and 2005, reinforcing his popularity with New Zealand fans who attended the circuit in large numbers.
In November 2003 Murphy won the Bathurst 24 Hour alongside Peter Brock, Jason Bright, and Todd Kelly in a Garry Rogers Motorsport-built Holden Monaro 427C, winning by just 0.35 seconds after 527 laps.
Murphy was championship runner-up in 2002 and 2003 while at Kmart Racing. After competitive peaks in the early 2000s, his results became less consistent following moves to Paul Weel Racing in 2005-2006, Tasman Motorsport from 2007, and Paul Morris Motorsport in 2010. Kelly Racing signed him for 2011 in a deal with Pepsi Max as major sponsor, and Murphy qualified on pole for that year's Bathurst 1000 and finished third.
He competed in the V8SuperTourer series in New Zealand from 2012, winning the championship in 2013 and again in 2014. His final starts in the Supercars Championship came in 2013 and 2014 as a co-driver alongside James Courtney at the Holden Racing Team, though both endurance campaigns were disrupted by incidents.
In 2021, backed by Boost Mobile and run by Erebus Motorsport, Murphy was confirmed to return to the Bathurst 1000 alongside compatriot Richie Stanaway as a wildcard entry. The 2021 attempt was postponed due to travel restrictions between Australia and New Zealand, but the wildcard was revived and contested at the 2022 Bathurst 1000.
Murphy ranks among the three most successful New Zealand drivers in Bathurst history, behind Jim Richards and Steven Richards. His 2003 qualifying lap remains one of the sport's most iconic single laps, and his four Bathurst victories placed him in elite company. His association with car number 51, used continuously from 2001, became one of the sport's most recognisable liveries.