It was the furthest Wigan have ever reached in any major cup competition and no-one can deny them a thoroughly deserved victory against their famous local rivals.
They were the better side for most of an enthralling contest and coped superbly with Bolton's familiar power play especially after the break when the visitors threw everything at them in a vain attempt salvage their own Cup dream.
After a lively opening in which both sides showed some flashes of neat football, it was Bolton who created the first real opening when Gary Speed latched onto a deep cross but saw his goalbound effort played off the line by Wigan full-back Leighton Baines.
Speed then shot straight into the grateful arms of Wigan keeper Mike Pollitt from close range before there were loud appeals for a penalty at the other end when Lee McCulloch appeared to be sent tumbling only for referee Mike Dean to dismiss the frantic shouts.
Wigan's Damien Francis then blazed over from long range before Kevin Davies planted a tame header into Pollitt's midriff when he should have done better.
But then, six minutes before the break, Wigan took a deserved lead following a delightful move.
A superb inside pass from Alan Mahon found Andreas Johansson, and when his cross found Roberts, the striker turned his marker before planting a firm drive into the bottom corner.
And then, right on half-time, Robert doubled the home side's advantage when he picked up a pass from Mahon after the little midfielder had carried the ball some 40 yards before blasting his and his side's second goal past Jussi Jaaskelainen.
If the home side expected their opponents to come out with all guns blazing in a bid to reduce the deficit after the break, then they were not disappointed.
Arjan De Zeeuw made a timely clearance to deny Stelios Giannakopoulos but it was the home side who came closest to increasing their lead when a vicious free-kick from Ryan Taylor appeared to be heading for the top corner only to be deflected for a corner.
Wigan's Graham Kavanagh was booked for a foul on Radhi Jaidi as an already tasty contest became even more spicy.
There were loud appeals for a Bolton penalty when De Zeeuw appeared to handle but again referee Dunn waved them away, and just minutes after coming on as a 56th minute substitute, Ricardo Vaz Te glanced a header just wide of the WIgan goal with Pollitt struggling.
But as Bolton poured forward Wigan began to find gaps at the back and Francis should have made the game safe in the 71st minute when he latched on to a delightful throughball from Baines only to see his shot tipped for a corner by Jaaskelainen.