The supermarket chain will also reduce diesel prices at its 223 forecourts by up to 1p, to a maximum of 138.7p.
Asda said the cut was due to a fall in wholesale prices, which had followed a series of rises over the summer caused be hikes the cost of in crude oil.
Andy Peake, Asda’s petrol trading director said: “We’re giving our customers the opportunity to fill up their cars with lower-priced fuel, putting much needed cash back in their pockets.”
The Automobile Association welcomed the “small but bold move in a period of turbulent wholesale prices”.
However, the motoring group warned drivers would still pay at least 3-4p more in areas without supermarkets which kept prices down.
President Edmund King said: “The reductions may look minor but, compared with the doom-and-gloom prices being predicted by the independent retailers in mid August, this is a significant change of fortune for UK drivers – albeit not all of them.
“The petrol price postcode lottery will ensure that many drivers will continue to pay up to £2 a tank more for petrol.
“With currently turbulent oil and wholesale fuel markets, we shouldn’t delude ourselves that prices can’t swing the other way again.
“But passing on the savings from this week’s fall in the cost of oil and fuel is bold and helpful.
“Other retailers would try to tie price cuts to spending in-store or sit tight hoping that local competitors don’t pass on savings at all.”
The AA’s latest monthly fuel price report, published on 14 August, showed Asda was the cheapest of 11 supermarkets and major forecourt chains such as Shell, BP and Jet.
The AA said the average UK petrol price yesterday was 138.16p, with diesel at 142.71p.
Petrol reached its highest price this year - 140.03p - in March, with the record high 142.48p in April last year.
Diesel reached 146.46p in March and a record of 147.88p in April last year.