Cabrera finished in fine fashion, going 4-under on his final four holes, after enjoying a day without a bogey.
After knocking it close for birdie on the par-3 15th, Cabrera rolled in a 15-footer at the 16th to get to minus-6. He had a chance for eagle at the par-5 17th, but his putt slid just left of the hole, for a tap-in birdie-4.
Cabrera, who won the Benson and Hedges earlier in the year, drained an eight-footer at the 18th to make it four consecutive birdies and a four-stroke lead.
'I started well and everything went perfectly after that,' said Cabrera. 'I didn't know that 62 was the course record. My only aim was to finish as well as I started and that's what happened with my four birdies at the end. I had a 61 last week in Italy but in view of the course, this must be one of my best rounds.'
Price, to be forever known as the man who took down Phil Mickelson at this years Ryder Cup, carded a 4-under 67 and is a shot clear of Simon Dyson, Brian Davis, Steen Tinning, Fredrik Jacobson and Bradley Drudge, all at minus-3.
Sergio Garcia is grouped in a tie for eighth with four other golfers, six shots off the pace, at 2-under. Garcia, ranked fifth in the world, started strong with birdies on three of his first four holes before a couple of bogeys at the seventh and ninth.
Garcia, who played alongside Colin Montgomerie, carded two more birdies and another bogey to end at minus-2.
Monty, looking to extend his streak of nine straight years with a victory, had an up-and-down day. Five birdies, two bogeys and a double-bogey left him seven back of Cabrera.
The final event of the year on the European Tour brings together the tours top 66 players, with this year having Retief Goosen and Padraig Harrington coming down to the wire for the right to the Order of Merit (money list).
Some of the luster of that battle was wiped away on Day 1 as both Goosen and Harrington struggled with their games, Goosen posting a 2-over 73 and Harrington carding a 3-over 74.
Though the quest for the Order of Merit will continue through the weekend ' there is no cut at this event ' they likely have both shot their way out of a chance for winning the tournament.
At the first hole, Harrington incurred a two-stroke penalty when he repaired a pitch mark on the fringe while his ball was on the putting surface.
'These things happen,' said Harrington, the defending champion. 'I just walked up and fixed the pitch mark which looked like it was on the green because of the shade. As I was digging there seemed to be a little more grass than you would expect and a bell went off in my head. I knew the rule and obviously it was a two-shot penalty.'
Full-field scores from the Volvo Masters