Westwood finished tied for second in the European Tour event in Dubai, with Rafael Cabrera-Bello winning by one stroke. McIlroy wound up tied for fifth after sharing the tournament lead after two rounds.
Cabrera-Bello jumps from 119th to No. 60 in the rankings, which were updated Monday.
Phil Mickelson won the PGA's AT&T Pebble Beach National Pro-Am and goes from 17th to No. 11 in the rankings.
Donald, now with a rankings points average of 9.423, has held the top spot for 37 weeks. Only six players have been No. 1 more weeks.
Westwood now averages 7.930, barely ahead of McIlroy's 7.925. Martin Kaymer (6.077) is fourth and Steve Stricker (5.770) remains fifth.
Webb Simpson has an average of 5.237 and is sixth ahead of No. 7 Jason Day (5.194) and eighth-ranked Adam Scott (5.094). Charl Schwartzel (4.932) remains ninth and Dustin Johnson (4.844) completes the Top 10.