Ffion Morgan and the recalled Ceri Holland each won 50th caps as part of a strong Welsh starting line-up, with Wilkinson sending out most of her big hitters in pursuit of a result.
The versatile Holland was typically influential before injury forced her off in the second half, with her volleyed cross leading to Wales' opener.
Viola Calligaris only succeeded in heading the ball upwards in her attempt to clear, leaving Ingle to head home from point-blank range.
Wales were undone too easily as Csillag beat goalkeeper Safia Middleton-Patel at the near post, yet they did not lose momentum.
Ingle's clever free-kick from deep in her own half sent Cain scampering in behind to score her fifth international goal, before half-time substitutes Woodham and Laura Hughes made an instant impact.
Debutant Hughes, the one-cap Australia international who has switched allegiances to Wales, was involved down the right before Woodham swept in from Cain's low cross.
Switzerland's second goal came as Wales tried and failed to play out from the back, with Manchester City teenager Beney finishing precisely from the edge of the area after Angharad James was unable to control Middleton-Patel's heavy pass.
But after Beney skewed another effort wide late on, Wales could celebrate a win which had been a long time coming.