Roared on by a packed crowd at Eton Dorney, Glover and Stanning won the opening heat of the Olympic regatta in a time of 6:57.29, beating the previous best by over four seconds.
Glover and Stanning controlled the race from the outset, leading the field by a half a length at the 500 metre time-check before pulling smoothly clear to beat the USA crew by a length.
The defending Olympic champions Romania came a surprise third and will have to negotiate the repechage to reach Wednesday's final.
Glover and Stanning reacted to being pipped into silver place at the 2011 World Championships by dominating the women's Pair this year, winning gold at all three of this summer's World Cup regattas.
If they can continue that run of success into Wednesday's final they will become Britain's first-ever female Olympic Rowing champions.
This performance sent out a powerful message of intent to the rest of the field, with heat two winners Australia coming home in a time four seconds slower than the British crew.
New Zealand, who beat Glover and Stanning by eight hundredths of a second to win the World Championships last year, trailed home unconvincingly behind the Australians.
"It was definitely a heats race for us," Stanning said. "It was a solid performance. We felt quite controlled in our boat.
"We have a final to come and that is where we will pull out all the stops."
Great Britain's men's Eight finished second in their heat behind three-time world champions Germany and will have to go through a repechage on Monday to reach Wednesday's final.
The repechage will give Britain an extra race together. They should enter Wednesday's final with podium potential and, following this performance, gold medal aspirations.
The race was five seconds faster than the first heat, which was won by a resurgent United States crew, who had finished eighth at the World Championships and qualified for the Olympic Games at the last opportunity.