Saints looked to be heading for a much-needed win when left-back Dan Harding scored from close range in the 73rd minute after good play from Rickie Lambert.
With 10 minutes to play the Bees were on level terms when Ryan Dickson surged down the left flank before crossing for Taylor to convert with an impressive diving header.
The hosts pushed forward in search of a winner late on and came close through Morgan Schneiderlin, but Brentford goalkeeper Lewis Price dived to his right to keep the strike out.
Saints had the best chances of the match and should have been ahead after 37 minutes but Neal Trotman managed to head over the crossbar from two yards when it looked easier to score.
Kelvin Davis made a smart save to deny Kevin O'Connor while Myles Weston smashed the ball over the crossbar after breaking clear in first-half injury time.