Gauci is one of Australia's most successful and durable jockeys. He won the Senior Victorian Jockeys Premiership in 1983-84, 1985–86, and 1990–91. He has come close to winning Australian racing's greatest prize on three occasions, with seconds in the Melbourne Cup on Chagemar (1984), Super Impose (1989), and On A Jeune (2005).
Gauci has been successful in 35 Group 1 races. For several years, Gauci also rode with great success in Hong Kong. Gauci won five races on trainer Lee Freedman's champion Super Impose, including an Epsom Handicap (1990), and rode Lonhro to victory in the Caulfield Guineas (2001) and the St George Stakes (2004) in his two rides on the "black flash". In an extensive association with trainer John Hawkes, he also won the Thousand Guineas on Shame (1995), a Doncaster Handicap on Over (2000) and a Stradbroke Handicap on Crawl (2001), but the partnership was terminated in 2005.
At the 2005 and 2006 Spring Carnivals, in Melbourne, Gauci won a feature race on El Segundo, and was narrowly beaten in the Cox Plate.
Over the years Gauci has had a number of bad riding injuries. For example, when he was in his early twenties, Gauci fell at Yarra Glen races and slipped in and out of a coma for eight days. In June 2011, at Mornington race course, the horse he was riding had a heart attack under him, crashed through the running rail, collapsed and died. Darren suffered very severe injuries and he did not recommence riding for ten months.
Despite his experience and skill, Gauci does not get rides on prominent horses as much anymore. However Darren says he understands that this is the reality and still enjoys his riding. Gauci said "As you get older it's a little bit harder, people put you on the back-burner a bit, they say you've been there, done that, probably had enough" .."I still love riding — I just do a lot more of it now, it's every day, and night."
A glimpse of the 'glory days' occurred at Wodonga, Australia on 2 June 2013, when Gauci rode a 'treble'.
As at 14 December 2013, Gauci had ridden in 7048 races and been placed in 1904 races including 669 wins. Total prize money won by horses ridden by Gauci is almost $36 million. Gauci retired from riding in February 2017 to take up a role as apprentice jockey coach with Racing Victoria. In a fairy tale ending to his distinguished career, Gauci rode a $17 winner on his last day of riding, the prophetically named Goodwill for owner Lloyd Williams.
Gauci is married to Karen (formerly Karen Dunkerton) whom he met when he made a guest appearance on the television show Young Talent Time in 1983. Karen was a member of the Young Talent Time team at that time and the 'starlet and the jockey' story created significant local media interest. They married in 1989 and have four children Jade, Breanna, Sean and Brooke.
In 2000, a portrait of Gauci was hung in the Archibald Prize competition.
He is of Maltese origin.