Back from his three-game suspension, during which Wigan have drawn one and lost two, Roberts pounced after 15 minutes of an entertaining clash when he picked up Jimmy Bullard's throughball, used his strength to hold off a challenge from Calum Davenport and slotted the ball passed Scott Shearer.
It was a goal that Wigan deserved after a lightening start against the division's form team and there was more to come seven minutes later, when Roberts seized on a weak header from Mo Konjic to drill the ball past Shearer.
Wigan might have had more goals in a 45 minutes that they dominated and only smart saves from Shearer denied Roberts a hat-trick and Lee McCulloch a goal.
But the home side lost their way playing a fierce wind in the second half as Coventry began to show the form that has taken them to the edge of the play-off positions.
Julian Joachim went close and Wigan keeper John Filan was in constant action as the visiting attack began to find its range.
They got their reward in the 72nd minute when the home defence failed to clear a corner and Stephen Warnock rifled the ball through a crowd of players and into the net.
The visitors pushed for an equaliser and they left a number of scars in the Wigan defence, while at the other end Shearer produced yet another cracking save to deny McCulloch.
The Sky Blues almost snatched the points at the death, only for while Matt Jackson to come to the home side's rescue with a last-gasp block to deny Brian Kerr.