The Californian overtook the second-leg winner, Gunnar Krantz's Swedish Match, just 50 miles from the finish of the 2,250 mile course from Fremantle to Sydney and then held on to win by just over five minutes.
Behind them, in rapid procession, the rest of the fleet came home in the early hours of a warm Sydney night. The first five boats all crossed the line within 10 minutes.
Added to his win on the first leg from Southampton to Cape Town, the second victory and the convoluted points system puts Cayard in the overall lead.
The former overall leader, Knut Frostad, was pipped for fourth place by Grant Dalton in Merit Cup and moves down to second. With Dalton also now fourth overall, Krantz moves up to third.
The all-round strength of Cayard's campaign is now acknowledged by all his rivals. A pecking order is beginning to emerge - and he is at the head of it. He learned his Southern Ocean lesson in a difficult baptism and his predictions of the growing importance of short course skills in ocean racing have been proved true. He is also setting a pace which has a few heads being scratched. Dalton was entirely frank, saying that the opening few days upwind were not what his boat was designed to enjoy. At least he is hanging on to the lead group.
Looking more glum was Britain's Lawrie Smith, who finished seventh and slipped to sixth overall. His crewman, Neil Graham, said: "You need a few breaks. There were a lot of position changes and we were on a snake rather than a ladder at the end."
Smith explained that, having been in third place, they had suffered some bad luck, ripping a much-needed spinnaker at a vital time, and had made a tactical error by working the shoreline for the last 100 miles when it would have paid better to go offshore.
Much happier was the American George Collins, joining his Chessie Racing for the first time in the race and seeing an improvement to third on the leg and up to fifth overall. The race restarts on 4 January.
WHITBREAD ROUND THE WORLD RACE Third leg (2,250 nautical miles, Fremantle to Sydney, finishing positions): 1 EF Language (Swe, P Cayard) 9 days 9hr 9min 20sec; 2 Swedish Match (Swe, G Krantz) 9:9:14.28; 3 Chessie Racing (US, G Collins) 9:9:15.21; 4 Merit Cup (Monaco, G Dalton) 9:9:17.37; 5 Innovation Kvaerner (Nor, K Frostad) 9:9:19.18; 6 Toshiba (US, P Standbridge) 9:9:30.4; 7 Silk Cut (GB, L Smith) 9:9:35.1; 8 Brunel Sunergy (Neth, R Heiner) 9:10:0.4; 9 EF Education (Swe, C Guillou) 9:10:47.32.Reuse content