The double world champions destroyed the previous mark, set by Germany in Barcelona 20 years ago, by nearly five seconds as they won their heat in 6:44.33.
It was a commanding performance from Grainger and Watkins, who left world bronze medallists New Zealand trailing home in second place around two lengths behind.
The British Double Scull pair are now unbeaten in 22 consecutive races and their victory will have laid down a marker to their nearest rivals Australia, who pushed them close in the final of last month's Munich World Cup regatta.
The Great Britain men's Eight qualified for the Olympic final with a victory over Canada and Netherlands in today's repechage.
The new-look Great Britain crew made a fast start and quickly opened a three-quarter-length lead over reigning Olympic champions Canada to take control of the race.
The Canadians, Holland and Australia all put the pressure on in the final stages and succeeded in closing the gap.
But Britain remained calm, rowing within themselves at 36 strokes per minute to seal the win and a place in Wednesday's final.
The British women's Quadruple Scull squeezed into their Olympic final after battling back from the brink of elimination to finish third in this morning's repechage.
They were trailing last in the six-boat field around the half-way mark before producing a strong push in the second 1000m.
Britain moved into the qualification places after the New Zealand crew developed a crab - where a rower's oar blade sticks in the water and acts as a brake - and then overtook reigning Olympic champions China to cross the line third, behind Australia and the USA.