As it was, Frank Lampard, Didier Drogba and an own goal sealed Wigan's fate and plunged them towards the relegation zone of the Premiership.
With Andriy Shevchenko apparently suffering from a hamstring injury, Jose Mourinho welcomed back Robben to the wing and continued with the mis-firing Salomon Kalou in attack.
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A fine left-wing move involving Robben and Wayne Bridge saw the England left-back race into the Wigan area on 11 minutes and arrow across a fine left footer which Drogba did well to get his left foot to. Unfortunately for the Ivory Coast hitman, his shot inched past Chris Kirkland's right-hand upright.
But two minutes later Chelsea took the lead through a complete mix-up between Kirkland and Fitz Hall. A respectable Lampard free-kick bounced on the six-yard line and dropped into the left-hand corner of Kirkland's net with both defender and goalkeeper expecting each other to clear.
Robben, just back from injury, produced a moment of magic on 24 minutes when he jinked past three Wigan players before receiving a one-two from Drogba inside the penalty area, but a byline cross was cleared by Lee McCulloch before Michael Ballack could head home.
A well-worked free-kick by Drogba and Lampard on 32 minutes saw the England midfielder fox the Wigan defence and he let fly from 20 yards but Kirkland responded well by tipping the ball past his post for a corner.
Wigan started the second half in determined mood and Bridge did remarkably well to hack away a Kevin Kilbane effort on goal on 52 minutes.
But goal number two was inevitable and another gift for the Blues. On 63 minutes Kristofer Haestad took it upon himself to roll a back pass to his goalkeeper but staggeringly under-hit it.
In stepped livewire Robben, who pounced on the ball, ran into the area and easily side-stepped Kirkland before slotting home with a cool right-footer from eight yards out.
Robben had another fine left-footed shot from the edge of the area saved by Kirkland on 68 minutes before he tore the Wigan defence apart and forced an error from Kirkland, who allowed the Dutchman's low drive to be deflected into the empty net for number three.
With the game won Mourinho rang the changes, bringing off star man Robben under-performing Kalou and full-back Paulo Ferreira.
Paul Jewell did the same bringing on Andreas Johansson, Denny Landzaat and Ryan Taylor.
Number four for the champions came from the head of top-scorer Drogba in injury-time as he dived to meet a fine right-wing cross from substitute John Obi Mikel.