White started the day with a lead of nearly a minute, but lost time early with electrical problems in his Lamborghini Gallardo, allowing Quinn's Nissan GT-R to move closer.
Overnight Classic Outright leader, Barry Faux, lost the top spot today as South Australian, Craig Haysman, driving a 1981 Triumph TR7, made the most of his local knowledge to move into a 30 second lead.
In wet conditions, problems with White's windscreen wipers made for an interesting drive, but once those gremlins were sorted the reigning champion was able to maintain his advantage.
Quinn had a trouble-free day and is over three minutes clear of the leading South Australian, Matt Selley, in a Mitsubishi Lancer Evo IX.
West Australian, Peter Rullo (Nissan GT-R), is in fourth place, with a further three minutes back to local driver, Andrew Burnard, in a Mitsubishi Lancer.
After suffering from engine and electrical problems over the eight stages of the first day, former South Australian, Steve Glenney, had planned a big attack on day two.
However, his charge was short-lived when he clipped a bank with the rear of his Subaru and gently rolled the car once. Although panel damage was minimal, the car suffered suspension damage and was forced to retire from the day's action.
In the Classic Outright competition, Haysman leads from Faux, while another local, Roger Paterson, dropped a spot to fourth during the day as West Australia ace, Tolley Challis, moved to third in his similar 1974Â Porsche, followed by Nick Streckeisen in fifth.
Bill Brentzell (1965 Shelby GT350) is leading the Shannons Early Classic competition ahead of Rob Black, while Bruce Power (Mazda RX7) has moved ahead of his fellow Canberra competitor, Barry Faux, in the Late Classic section.
Tim Possingham (Nissan) has extended his lead in the Early Modern section, with the battle for second place hotting up between David Welling (Mitsubishi Lancer ), Adam Kaplan (Holden Commodore), and Andre Lukasz (Nissan 200 SX).
Another driver to have maintained his lead over day two was Greg Burrowes in the Supaloc Showroom 4WD competition. His Lancer Evo X is a minute clear of another three Mitsubishis, with Mark Rundle the best placed, in second.
Glyn Crimp (Showroom) and Neill Ford (Showroom Sports) also continue to lead.
Supaloc Targa Adelaide
Results after Day 2
SUPLOC MODERN
1. Jason White / John White, 2011 Lamborghini Gallardo, 14m33s
2. Tony Quinn / Naomi Tillett, 2011 Nissan GT-R, +40s
3. Matt Selley / Hamish McKendrick, 2005 Mitsubishi Lancer Evo IX, +3m41s
4. Peter Rullo / Simon Iseppi, 2012 Nissan GT-R, +3m49s
5. Andrew Burnard / Tim Magarch, 2004 Mitsubishi Lancer Evo VIII, +6m47s
SHANNONS CLASSIC OUTRIGHT
1. Craig Haysman / Neil Branum, 1981 Triumph TR7 V8, 23m17s
2. Barry Faux / Therezia Mihajlovic, 1979 Mazda RX7, +30s
3. Tolley Challis / Greg Flood, 1974 Porsche 911 Carrera RS, +58s
4. Roger Paterson / Paul Whatnell, 1974 Porsche 911 RS, +1m37s
5. Nick Streckeisen / Mike Dale, 1985 Porsche 944 Turbo, +1m39s
SHANNONS EARLY CLASSIC HANDICAP
1. Bill Brentzell / Karien Heimsohn, 1965 Shelby GT350, 20m09s
2. Rob Black / Vivek Ponnusamy, 1971 Porsche 911 S, +2m48s
=3. Jack Waldron / Vin Gregory, 1955 Fiat Abarth 750, +4m10s
=3. Andrew Bryson / Craig Milich, 1964 Hillman Imp Rallye, +4m10s
5. Richard Woodward / Neil Gibson, 1969 Holden Monaro GTS, +4m29s
SHANNONS LATE CLASSIC HANDICAP
1. Bruce Power / Ray Baker, 1979 Mazda RX7, 19m24s
2. Barry Faux / Therezia Mihajlovic, 1979 Mazda RX7, +04s
3. Nick Streckeisen / Mike Dale, 1985 Porsche 944 Turbo, +1m13s
4. Edward Yates / Rob McBrien, 1973 BMW 2002, +1m53s
5. Craig Haysman / Neil Branum, 1981 Triumph TR7 V8, +1m55s
SUPALOC EARLY MODERN
1. Tim Possingham / Ben Scott, 1990 Nissan Skyline GT-R, 19m55s
2. David Welling / Tristan Catford, 1999 Mitsubishi Lancer Evo VI RS, +3m52s
=3. Adam Kaplan / David Kaplan, 1988 Holden Commodore HSV, +4m30s
=3. Andre Lukasz / Adam Tillett, 1994 Nissan 200 SX, +4m30s
5. Charles Nott / Henry Nott, 1998 TVR Chimaera, +6m56s
SUPALOC SHOWROOM 4WD
1. Greg Burrowes / Rhonda Burrowes, 2009 Mitsubishi Lancer Evo X, 24m43s
2. Mark Rundle / Steve Fisher, 2003 Mitsubishi Lancer Evo VIII, +1m00s
3. Michael Flood / Nathan Green, 2012 Mitsubishi Lancer Evo, +1m50s
4. Allan Mair / Michelle Mair, 2005 Mitsubishi Lancer Evo IX, +6m36s
SUPALOC SHOWROOM
1. Glyn Crimp / Paul van der Mey, 2010 Ford Focus RS, 25m52s
SUPALOC SHOWROOM SPORTS
1. Neill Ford / Nathalie Ford, 2007 Chevrolet Corvette Z06, 28m05s
RDA BRAKES REGULARITY
1. John Goodall / Graham Palich, 2009 Porsche Cayman, 125 points
2. Richard Davis / Bill Best, 2008 HSV W427, 200 points
3. John Amos / Cintra Amos, 2009 Mitsubishi Lancer Evo X, 292 points