There were few clear-cut chances in a dull end-of-season encounter between two sides with little to play for.
But the deadlock was broken with six minutes remaining, when goalkeeper Jack Bonham was caught out by what looked like an attempted cross by Dasilva.
It was Dasilva's first goal of the season and came after Steven Fletcher had gone close with a couple of decent opportunities for Stoke.
Fletcher headed just wide from Tommy Smith's cross and sent an effort over the bar after the Robins were troubled by a cross from Mario Vrancic.
Fletcher also appealed in vain for a penalty following a challenge by Alex Scott as he attempted to get to a cross from Jacob Brown.