The midfielder got on the end of Matt Richards' free kick eight yards out on 71 minutes and the ball found the back of the net via a deflection, but Stanley were furious as they felt the foul shouldn't have been given as Peter Murphy appeared to win the ball.
It was always going to take just one goal to decide a disappointing game of few chances for the early season strugglers.
It was a largely forgettable first half with neither side really testing the keepers and the only incidents of note were bookings for Stanley's Michael Richardson and the Robins' Keith Lowe.
The second half warmed up a bit with Steven Gillespie curling wide and, on 51 minutes, Stanley keeper Ian Dunbavin was tested for the first time with a long range effort from Taylor.
Kal Naismith and Lawrie Wilson fired wide for Accrington - who have picked up just one point this season - in a clash of few openings.
Both managers changed their attacking line-ups as they looked for the all-important goal but it took Taylor to clinch it.
Stanley ended the game with 10 men, with Wilson going off injured with five minutes left after they had used all three subs.