It took Fletcher less than four minutes to get off the mark for the season after tapping home Stephen Pearson's shot, which had initially been kept out.
A quiet spell for both sides followed, but it was the visitors who continued to look the more lively as Marvin Johnson played in Fletcher, who failed to find the target with his 18-yard drive.
Johnson then tried his own luck from range, having already advanced from the halfway line, only for his effort to deflect behind.
Fon Williams took no chances when an early Johnson shot called him into action in the second half, before Devine pulled off a fine challenge to deny Fletcher from four yards out.
Well winger Johnson was proving to be a threat right to the end, cutting in from the right and sending a curled shot wide of target 10 minutes from time.
Nicky Law then saw a big opening of his own come and go in what proved to be the final chance of the contest in the dying embers, as the visitors left Caledonian Stadium with maximum points.