Raonic, at 22 almost 10 years younger than his unseeded Russian opponent, managed one break of the Davydenko serve to secure the first set and edged the second-set tiebreak 7-5 to set up a second-round clash against unseeded Spaniard Fernando Verdasco, whom he has never beaten on clay in two attempts.
"I've just got to clean up crucial mistakes, take care of my serve, create a couple of opportunities on his serve and make the most of them," Raonic, looking ahead to the Verdasco match, said on the ATP website (www.atpworldtour.com).
Kei Nishikori joined Raonic in the second round when he thumped Austria's Jurgen Melzer 6-3 6-2 as the Japanese 14th seed closes on a potential third-round meeting with world number two Roger Federer.
The Swiss, last year's Madrid Open champion, took a break after the Indian Wells Masters in March and returns to begin his title defence with a first-round match against Czech Radek Stepanek on Tuesday.
World number one Novak Djokovic and number three Andy Murray also play their first-round matches on Tuesday. Djokovic takes on unseeded Bulgarian Grigor Dimitrov, while Murray meets Germany's Florian Mayer, also unseeded.