Welch pounced with a shot off the left-hand post when Torquay failed to clear an Ian Craney corner in the 47th minute.
And Roberts wrapped up the points with a brilliantly taken second, twice beating Torquay defender Lee Andrews and then slotting the ball home after a Craney pass in the 72nd minute.
The result extended Torquay's losing run to four matches, but nobody could deny Stanley the result on the first-ever league game between the two clubs.
Torquay had the better of the first half and had at least three clear-cut chances to take the lead.
Mickey Evans twice and Lee Thorpe were denied by brave saves from Stanley keeper Ian Dunbavin and defender Leam Richardson.
But the best player on the pitch was Stanley left-winger Romuald Boco, who gave Andrews a torrid time throughout the match.
Boco's pace was a constant threat and he nearly scored with one blocked shot as well as setting up a half-chance for Andy Proctor.
If Torquay fans hoped that their side would turn pressure into goals in the second half then they were sorely disappointed.
Stanley dominated the second half, ruining the first day in charge for new Torquay owner Chris Roberts who only took control of the club earlier in the week.
A Thorpe header hit the post for Torquay, but Welch also struck the woodwork with an ambitious long range effort.
Boco then tested Torquay goalkeeper Nathan Abbey with two fierce shots.
Torquay boss Ian Atkins sent on all his substitutes - Chris McPhee, Lee Mansell and on-loan striker Leo Fortune-West - in an effort to salvage something from the wreckage but it was to no avail.