Nahki Wells had given the Terriers the lead early in the second half, but Woodrow climbed off the bench to grab a point as Fulham’s winless run continued.
It meant both Fulham and Huddersfield are are still yet to win in four league games, with Kit Symons, in his first full season, is coming under increasing pressure from the fans
It took just 18 minutes for the disgruntled home fans to turn on Fulham and by that time the hosts were lucky to still be level.
Jacob Butterfield, who had been the subject of failed bids from Derby County, saw his 25-yard shot turned away by Fulham goalkeeper Andy Lonergan with Harry Bunn unable to force the rebound home.
Fulham finally threatened when Dan Burn’s header was kept out by Joe Murphy in a rare attack.
The home side were getting nowhere against an organised Huddersfield side and Jamie O’Hara took matters into his own hands from long-range, with his effort kept out by another fine Murphy save.
Butterfield was catching the eye and impressive footwork saw him open up the opportunity to strike at goal where Lonergan was once again equal to his effort.
The hosts, however, looked a side devoid of confidence in a turgid opening period that saw them rarely threaten the Huddersfield goal. It was Chris Powell’s side who looked the more threatening, with Sean Scannell going close five minutes after half-time.
The winger benefitted from a fortunate rebound but his low shot lacked power and was easily gathered by Lonergan.
Fulham’s best hope of a breakthrough seemed to lie with a set-piece, and it nearly reaped rewards on the hour mark as Ross McCormack’s free-kick was met by a powerful header from Moussa Dembele, only for Murphy to deny the striker.
It proved crucial as Huddersfield went up the other end to take a 62nd minute lead via Wells, as the striker finished easily from Harry Bunn’s threaded through-ball.
The supporters soon made their feelings known, as the boos began to ring out around the ground. It could have been worse as Scannell’s header was kept out by Lonergan. From the resulting corner, Mark Hudson headed narrowly over from close-range.
Fulham were struggling to find a way through but they struck with almost the last kick of the game as Woodrow reacted first to a goalmouth scramble to claim a second point of the season.