All three were considered favourites going into the tournament, and will still believe they can mount a challenge with three days to play.
Westwood started the day well with a birdie at the first and another at the fifth, but bogeys seven, nine, 11 and 15 saw him drop off the pace before another birdie at 17 kept the Englishmen within six shots of the lead.
Masters champion Scott also had a mixed day going two-over par early on before a series of birdies got him back into contention.
A bogey at 10 and another on the final hole meant that the 33-year-old finished on level par.
Fourteen-time Major winner Woods is just ahead of his playing partner on two-under, after recovering from a penalty-drop at the first hole.
Woods's putting was a highlight for him, particularly around the turn, where he birdied 10, 11 and 13. Another birdie on 17 made up for an earlier bogey and a solid final putt saved par at the final hole to leave him within three shots of the lead.