Czech Berdych, who had a bye into the second round and is seeded three on the clay at the Real Club de Tenis, served poorly against the 31-year-old Russian, who had won nine of their 11 previous matches.
After having his service broken twice in losing the first set, Berdych managed to turn things around to edge the second before lifting his game in the decider and sealing victory with a ninth ace.
The 27-year-old will play the winner of the match between Bulgaria's Grigor Dimitrov, the 14th seed, and 2004 champion Tommy Robredo of Spain for a place in the quarter-finals.
Latvian qualifier Ernests Gulbis provided the surprise of the day when he thumped former world number seven and 12th seed Fernando Verdasco of Spain, who won the event in 2010, 6-3 6-4.
World number five Rafa Nadal begins his bid for an eighth Barcelona title in nine years with a second-round clash against unseeded Argentine Carlos Berlocq on Wednesday.
Recently back from seven months out with a knee injury, Nadal is seeded second and beat top-seeded Spanish compatriot David Ferrer, the world number four, in the final in 2008, 2009, 2011 and 2012.
Ferrer plays his second-round match against Russian qualifier Dmitry Tursunov on Wednesday.
In the doubles event there was a great win for British duo Colin Fleming and Jonathan Marray as they disposed of fourth seeds Aisam-Ul-Haq Qureshi and Jean-Julien Rojer 6-4 2-6 10-6.
ATP Barcelona results
3-Tomas Berdych (Czech Republic) beat Nikolay Davydenko (Russia) 3-6 7-5 6-4
8-Philipp Kohlschreiber (Germany) beat Andrey Kuznetsov (Russia) 6-3 6-7(5) 7-6(2)
Ernests Gulbis (Latvia) beat 12-Fernando Verdasco (Spain) 6-3 6-4
6-Kei Nishikori (Japan) beat Guillermo Olaso (Spain) 6-1 6-3
10-Jeremy Chardy (France) beat Paolo Lorenzi (Italy) 6-2 6-4
Albert Ramos (Spain) beat Jan-Lennard Struff (Germany) 6-4 7-6(2)
Tommy Robredo (Spain) beat Marc Lopez (Spain) 2-6 6-2 6-2
Blaz Kavcic (Slovenia) beat Alejandro Falla (Colombia) 6-3 6-0
Edouard Roger-Vasselin (France) beat Jan Hajek (Czech Republic) 6-2 6-7(1) 6-2
Bernard Tomic (Australia) beat Kenny De Schepper (France) 6-4 4-6 6-2
Carlos Berlocq (Argentina) beat Daniel Gimeno-Traver (Spain) 7-5 6-4
ATP Bucharest results
Victor Hanescu (Romania) beat Matthias Bachinger (Germany) 6-4 6-3
Guillermo Garcia-Lopez (Spain) beat 7-Horacio Zeballos (Argentina) 3-6 6-4 6-0
Santiago Giraldo (Colombia) beat Xavier Malisse (Belgium) 6-1 6-2
Lukas Rosol (Czech Republic) beat Gilles Muller (Luxembourg) 7-6(4) 6-2
Gael Monfils (France) beat Filippo Volandri (Italy) 6-4 6-2
Sergiy Stakhovsky (Ukraine) beat Jaroslav Pospisil (Czech Republic) 6-2 6-2
5-Florian Mayer (Germany) beat Flavio Cipolla (Italy) 6-0 7-6(1)
Jarkko Nieminen (Finland) beat Evgeny Donskoy (Russia) 1-6 6-4 7-6(3)
Tobias Kamke (Germany) beat Paul-Henri Mathieu (France) 6-1 6-3