Ryan Taylor hammered in the free-kick from his own half and Kilbane ghosted in ahead of Freddie Ljungberg on the corner of the six-yard area, and lifted the header over Robert Green.
Wigan were desperately unlucky not to get a second after the break when Antonio Valencia had the misfortunate to see his shot hit both posts and then bounce kindly into Green's arms.
And they also missed a clear-cut chance two minutes from time when Marcus Bent hammered over with only the keeper to beat.
The Hammers - previously unbeaten at the JJB Stadium and fresh from a 1-0 win over Liverpool - had produced the first threat in a scrappy first period after Wigan conceded a soft corner.
Mark Noble fired it into the danger area, the Latics failed to clear and Ljungberg forced a good save from Chris Kirkland.
Referee Martin Atkinson riled Wigan fans with handball decisions against Marlon King and Ryan Taylor, both in promising situations.
However, Wilson Palacios had to get in a timely tackle to deny Matthew Etherington a shot as the defence again had trouble dealing with Ljungberg's cross.
Wigan went close when George McCartney was penalised for a foul on King, and Taylor beat the wall with the free-kick but saw the shot fly just past Green's left post.
Taylor was given another opportunity when Matthew Upson brought down Valencia and whipped in an excellent free-kick but no-one got a touch as it whistled across goal.
Skipper Mario Melchiot tried his luck when Emile Heskey set up the shot but he hit it well over the bar.
Wigan had a penalty appeal turned down when King's shot hit Anton Ferdinand but they snatched the lead with that stoppage time goal, Kilbane's second since his arrival from Everton last season.
Wigan had another chance but Michael Brown's shot lacked power and came back off Green's legs.
But West Ham continued to look dangerous as they hunted an equaliser with Carlton Cole and Craig Bellamy failing to hit the target.