Lille took an early lead but struggled to hold off their neighbours in the closing stages of a lively game.
Valenciennes now lie sixth in the standings on 15 points, four behind leaders Paris St Germain who travel to bottom club Nancy later.
Lille, ninth on 14 points, started strongly as Roux opened the scoring in the second minute, firing home from close range following a poor clearance by the Valenciennes defence.
The visitors' hopes suffered a further blow in the 28th minute when Carlos Sanchez was sent off after picking up a second yellow card for a rough challenge on Florent Balmont.
They fell two behind four minutes before the break when Salomon Kalou dashed into the defence and set up striker Payet to calmly slot home with a low shot from inside the box.
Anthony Le Tallec pulled one back in the 71st minute when he tapped home from a Gael Danic cross.
Valenciennes increased the pressure in the last 15 minutes and had several chances but were denied by keeper Mickael Landreau.