Roberts scored the only goal of the game to power the Swans to an important away victory.
Andre Ayew who won the Man of the Match of the game took to his Twitter handle to express his joy.
“3 points away from home White circleBlack circlelove it!great shift guysRed heart we keep going.. Swan MOTM,” he tweeted.
Blow is the match report
Steve Cooper’s team are just two points adrift of leaders Norwich City after Roberts’ brave finish secured their third away league win of the campaign.
Wales defender Roberts rose high to put his team in front just before half-time and Forest could not find a response.
They were beaten at the City Ground for the first time under Chris Hughton, who had taken eight points from his four previous home games, and remain 21st in the table.
Hughton’s men asked questions at times but were kept at bay by Swansea who, having conceded only eight Championship goals in 2020-21, have the best defensive record in English football’s top four divisions.
They have lost only two of their 14 league games since defeat in last season’s play-offs and continue to look like a team capable of mounting another promotion push.
Forest began the contest with purpose, Sammy Ameobi making an early burst down the left before centring for Lyle Taylor, whose shot rolled across the face of goal.
Hughton has made Forest hard to beat on their own patch, and they were putting pressure on Swansea’s defence for much of the first half.
The hosts ought to have gone ahead on 39 minutes, when Anthony Knockaert cut in from the right flank on to his stronger left foot, only to drill a shot straight at Freddie Woodman, who kicked the ball clear.
Let off the hook, Swansea made Forest pay thanks to Roberts’ prodigious leap.
Andre Ayew lofted a hopeful ball into the penalty area which Forest centre-back Scott McKenna flicked towards the back post, where wing-back Roberts rose high above the 6ft 4in Ameobi to place a header beyond Brice Samba and put his team ahead.
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