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Roberts had missed a sitter against the champions but kept his nerve to supply a superb first-time finish to Brett Emerton's cross and wrap up victory.
Morten Gamst Pedersen had put Rovers in front eight minutes earlier when his free-kick from the byline eluded everyone in the box and curled into the top corner.
And despite Charles N'Zogbia reducing the deficit for Wigan with a 74th-minute free-kick, the visitors failed to muster another chance to snatch a vital point.
Last week's stirring but ultimately fruitless performance against Chelsea seemed a distant memory in a tepid first period which quickly seemed destined to finish goalless.
The home side's early chances came from Christopher Samba at set-pieces, while Wigan spurned the few chances they had, slamming two free-kicks into the Rovers wall.
N'Zogbia showed a flash of skill to burst into he box where he was dispossessed by Gael Givet, while at the other end Ali Al Habsi flapped at a Pedersen free-kick.
Mame Biram Diouf had the best early chance when he was played clear by Pedersen, only for the Wigan goalkeeper to burst from his goal and dive bravely at the striker's feet.
The more entertaining action came on the touchline where former Wigan defender Pascal Chimbonda was relishing the taunts of the visiting fans at the Darwen End.
Wigan had their first real shot on target in the 31st minute when Rodallega burst through on the left and hit a left-foot shot which Paul Robinson saved well.
And as the visitors ended the half strongly, Rovers had a lucky escape in the 38th minute when N'Zogbia barged through to put the ball in the net, only to be pulled up for a foul on Pedersen.
The visitors continued in the ascendancy at the start of the second period with N'Zogbia serving up fine crosses which Hugo Rodallega and Steve Gohouri failed to convert.
But Al Habsi had to perform heroics to keep his side level in the 49th minute when Pedersen met Brett Emerton's deep cross from the right and the goalkeeper made a superb reaction save.
Rovers grabbed the lead in the 58th minute when Pedersen's free-kick from out on the right touchline evaded everyone and curled into the top corner past a helpless Al Habsi.
The visitors had a half-hearted penalty appeal turned down when Rodallega tripped over Givet, but Rovers went further ahead in the 66th minute when Emerton crossed from the right and Roberts beat the offside trip to slide home.
Wigan still looked lively and reduced their deficit when N'Zogbia drilled a low free-kick in off Robinson's left-hand post in the 74th minute.
Rodallega's effort from an N'Zogbia cross was blocked in the box but Wigan failed to muster any further chances and gave the home side a comfortable last quarter of an hour.
Rovers should have extended their winning margin deep into injury time when Chimbonda crossed to David Dunn, but he contrived to slice wide the simplest of chances.