Navarro, a Spaniard ranked No. 104 in the world, battled for two hours and 36 minutes before falling to the Russian. Navarro used an unusual serve-and-volley game on the slow clay court to surprise Davydenko and also played many drop shots from the baseline to mix things up.
"It's not simple to play against him," Davydenko said. "The first couple of matches in a tournament are usually tough for me."
Fourth-seeded Victor Hanescu of Romania also advanced to the second round by beating qualifier Dominik Meffert of Germany 6-4, 7-6 (6), while Lukasz Kubot of Poland beat Pablo Andujar of Spain 6-2, 6-4 in a match between two qualifiers.
Germany's Michael Berrer rallied from losing the first set 6-0 to beat Austria's wild card entrant Stefan Koubek 0-6, 7-6 (3), 7-6 (4).
Szavay wins Budapest title by beating Schnyder
