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.