Nadal, the defending champion and No. 2 seed this week, came back for a 3-6, 6-2, 6-3 win over Marcos Baghdatis while Davydenko needed a total of 37 games and one tiebreaker over nearly three hours to get past Younes El Aynaoui 6-7 (2-7), 7-5, 7-5.
Also in Tuesday's first-round play, Daniele Bracciali defeated Oliver Marach 6-4, 6-3; Rainer Schuettler topped Andreas Seppi 6-0, 7-6 (7-5); Gilles Simon beat Philipp Kohlschreiber 6-4, 6-4; and Mikhail Youzhny was a 3-6, 6-3, 6-3 winner over Jarkko Nieminen.
The tournament continues through the week. The champion of the Dubai Open will win $300,000.