The firm, which has 4.5 million household customers, said the move is equivalent to £24 off the average annual gas bill, or two weeks’ gas use.
E.ON UK chief executive Tony Cocker said Labour’s proposed “price freeze” meant the company was “undoubtedly taking a risk” by cutting tariffs.
Labour wants to give regulator Ofgem the ability to force companies to pass on falls in the price of wholesale oil and gas to consumers, which industry estimates claim could knock £136 off the average bill.
E.ON also launched what it said was the country’s cheapest energy tariff, a new one-year fixed dual-fuel product with an average annual price of £923.
Mr Cocker said: “Today’s 3.5% cut to our standard gas price and the launch of the UK’s cheapest energy tariff, our one-year fixed product, demonstrate that we fundamentally believe in doing the right thing for our customers.”
The move increases the pressure on the other Big Six energy suppliers - British Gas, SSE, Scottish Power, EDF and npower.
Mr Cocker said: “Given the possibility of a price freeze, we are undoubtedly taking a risk today but we always put our customers first. That was in the forefront of our minds before Christmas when we began the detailed process of delivering today’s price cut.
“We have made this decision knowing that our ability to recover costs, should the market outlook change in the months or years ahead, may be limited but we urge all political parties to recognise the realities of the energy industry and help us to continue to do the best for all of our customers.”
Last January E.ON became the last of the Big Six firms to raise gas prices, by 3.7% or £20 a year.
However, year-forward wholesale gas prices have fallen 28% over the last 12 months, according to consumer body energyhelpline.com.
Its marketing director, Mark Todd, said E.ON’s move was a “small step in the right direction”.
He added: “British Gas in particular should be able to follow quickly and with bigger cuts. They have the highest standard gas prices and benefit the most from wholesale gas price drops.
“Now is the time for suppliers to take action. Winter is here and this is when customers most need a price cut but suppliers with an eye to profit least want to give one. The reaction of the other suppliers will show their priorities - customers or profit.”
Industry regulator Ofgem wrote to the Big Six firms in the summer, asking them to explain how they were going to pass on falling wholesale costs to their customers. It also referred the industry to the Competition and Markets Authority.
In July the Competition and Markets Authority (CMA) launched a wide-ranging investigation into the UK’s energy market which will look at rising energy bills, service quality, profitability and uncertainty over future investment.
Mr Cocker said he hoped the outcome of the Competition and Markets Authority probe would bring certainty into the market.
He said: “This includes all parties committing to accept the outcome of the current Competition and Markets Authority investigation into the energy industry when that completes at the end of this year to provide energy companies with the all-important political and regulatory certainty we need in order to be able to plan and run our businesses efficiently.”
Energy Secretary Ed Davey said: “This will be very welcome news for many bill-payers. Those who aren’t seeing price cuts should check whether someone else can give them a better deal - many people have saved hundreds of pounds by switching supplier, which is now quicker and easier than ever before.”
He added: “The best deals on the market are cheaper than they were a year ago, which shows the Government’s reforms to the energy markets are working to get a better deal for consumers.”