The Scots made a better fist of things in the second spell to restrict Wales to two penalties by Evans in the 41st and 76th minute.
The game was only three minutes old when Evans knocked over her first penalty. Good support work by the flying Evans put Wright over in the 14th minute to give Wales an 8-0 lead.
Scotland responded in the 22nd minute with a penalty by Sarah Gill but that was quickly cancelled out by another Evans penalty two minutes later.
Wales continued to dominate to see Berry romp home from 30m after good leadup work by Rachel Poolman and with Evans adding the conversion, Wales held a comfortable 18-3 advantage.
Scotland got back into the game when Lucy Millard touched down to give Gill an easy conversion but with six minutes remaining of the first half, Evans finished off a move in clinical fashion. With Evans knocking over the conversion, Wales were in control at the interval.
Wales failed to ram home their advantage in the second half but coach Jason Lewis was still a pleased man after the game.
"It was important we got our campaign off to a winning start," he said. "To come to Scotland and win 31-10 is no easy task. It was disappointing we let things slip in the second half and we won't be able to do that against England next week. But with regards to qualification for next year's World Cup, it was a good start."
Wales skipper Mellissa Berry, who claimed her 70th cap, and her 50th as captain, echoed her coach's sentiments.
"It was important we got our campaign off to a win," she said. "To have such a healthy lead at halftime was very pleasing whereas the second half wasn't as good but it gives us something to build on for the rest of the campaign."