Di Canio resigned on Monday citing off-field troubles at the club but it failed to halt the Robins on the pitch with James Collins putting them ahead soon after the break.
Roberts volleyed in a fine first from 25 yards before Donervon Daniels pulled one back.
But Roberts then netted from inside his own half to condemn Tranmere to a fourth consecutive defeat.
Swindon began the brightest and Miles Storey poked wide before Collins failed to find the target after goalkeeper Owain fon Williams fumbled in his area.
The Robins went ahead after 48 minutes, top scorer Collins beating fon Williams to a Simon Ferry through ball before finishing calmly into an empty net from the edge of the box.
Roberts then hammered in a stunning volley from 25 yards after 71 minutes before Daniels netted seven minutes later from Max Power's free-kick.
But Roberts settled it in style after fon Williams came up for a late Tranmere corner only for it to be cleared, allowing the Swindon man to shoot home from inside his own half.
In the night's other League One match, Oldham came from behind to win 2-1 at Stevenage.
James Dunne put the hosts ahead in the ninth minute but Dean Furman and James Tarkowski struck after half-time to clinch all three points.