Hundreds of his signature stick figures can be seen gathered at a match on a washed-out looking pitch between terraced houses and factories with billowing chimneys. The painting has been described as 'a modern masterpiece'.
The Football Match had been estimated too high at £3.5 million to £4.5 million.
The existing record for Lowry was £3.8 million, set at the market peak in 2007.
However, three bidders ran the price up until it sold to an anonymous private European buyer for £5.6 million.
The price, significantly, was greater than those for any Henry Moore sculpture or Damien Hirst painting at auction.
One auction house has sold 125 of his works since June 2006, together totalling £29.4 million.
The highest price for a Lowry football painting was £1.9 million when Going To The Match was sold in in 1999.
Like the work to be sold on May 26, the canvas was 28 x 36 inches.
'The Football Match by L.S. Lowry is the ultimate work for passionate connoisseurs of Lowry's work and of football.'
Rachel Hidderley, international specialist in 20th century British art, added: 'The large format, panoramic, bird's-eye composite view
of Lowry's own landscape perfectly captures the spirit and drama of a town
gripped by the excitement of the Saturday football match.