Nathan Ellington opened the scoring, side-footing home a low cross from Gary Teale that eluded three Leeds players.
Lee McCulloch missed two great chances, while Neil Sullivan saved from Jimmy Bullard and Roberts - but the Wigan striker eventually made it 2-0.
Roberts diverted McCulloch's goal-bound header past Sullivan and hit the foot of the post later on before Alan Mahon scored from 30 yards.
Leeds boss Kevin Blackwell on the on-field row between Gary Kelly and Sean Gregan:
"They want to give everything they can for this football club. I want players to nail other players if they are not doing it.
"It's not always up to the manager, you need players to do that sometimes.
"But I take my hat off to Wigan, they were a cut above. They've set a benchmark we now have to attain."
Wigan: Filan, Eaden, Breckin, Jackson, Baines, Teale, Bullard, Mahon, McCulloch, Roberts (Graham 83), Ellington (Jarrett 87).
Subs Not Used: Walsh, Wright, Whalley.
Booked: Roberts.
Goals: Ellington 10, Roberts 56, Mahon 75.
Leeds: Sullivan, Kelly, Carlisle, Butler, Gray, Wright (Richardson 63), Gregan, Derry, Lennon, Hulse, Healy.
Subs Not Used: Ricketts, Walton, Johnson, Deane.
Booked: Hulse, Derry.
Att: 17,177.
Ref: P Joslin (Nottinghamshire).