Westwood, ranked third in the world and seeking his second victory on U.S. soil, shot a 2-under 68 at the TPC-Southwind course to finish 36 holes at 131. Willis equaled the day's low score with a 65 Friday.
The 36-hole cut came at 1-over 141 and among those missing it was 16-year-old amateur Jordan Spieth. He finished among the top 20 at the Byron Nelson Classic last month, but failed by a single shot to make the cut this week.
John Daly survived the cut with a 141 total.
This is the final PGA Tour event before the U.S. Open, which will be played for the fourth time at the Pebble Beach Golf Links beginning next Thursday.
2014: The Year in Music [PHOTOS]