World number 147 Evans was disappointed to have been left out of the Davis Cup team which beat USA in San Diego at the weekend, with 175th-ranked James Ward earning the spot ahead of him.
But he made up for it with an easy win against world number 106 Hajek - and in Berrer will face a player who is one spot below him in the ATP rankings.
Fifth seed Marin Cilic reached the quarter-finals with 6-4 7-5 victory over Dusan Lajovic but Lukas Rosol, the number six seed, crashed out after a 6-3 7-6(2) first round defeat at the hands of Dudi Sela.
"It wasn't an easy match," said Cilic. "Lajovic played pretty solid today and he proved that he's a promising player. I served pretty good and kept my service games out of danger.”
ATP Zagreb Round 2
5-Marin Cilic (Croatia) beat Dusan Lajovic (Serbia) 6-4 7-5
8-Igor Sijsling (Netherlands) beat Blaz Kavcic (Slovenia) 6-7(4) 6-3 6-4
Andrey Golubev (Kazakhstan) beat Victor Hanescu (Romania) 7-6(6) 4-6 7-6(5)
Andrey Kuznetsov (Russia) beat Sergiy Stakhovsky (Ukraine) 6-4 7-6(8)
Dudi Sela (Israel) beat 6-Lukas Rosol (Czech Republic) 6-3 7-6(2)
Daniel Evans (Britain) beat Jan Hajek (Czech Republic) 6-3 6-1
ATP Montpellier Round 1
7-Edouard Roger-Vasselin (France) beat Michal Przysiezny (Poland) 7-6(3) 6-3
Nikolay Davydenko (Russia) beat 8-Julien Benneteau (France) 7-6(6) 7-5
Dustin Brown (Germany) beat Teymuraz Gabashvili (Russia) 4-6 6-1 7-6(1)
5-Gael Monfils (France) beat Lukasz Kubot (Poland) 6-4 4-6 6-3
6-Jarkko Nieminen (Finland) beat Aleksandr Nedovyesov (Kazakhstan) 4-6 6-2 4-4 (Nedovyesov retired)
Joao Sousa (Portugal) beat Tobias Kamke (Germany) 3-6 6-1 6-4
ATP Vina del Mar International Round 2
Santiago Giraldo (Colombia) beat 4-Marcel Granollers (Spain) 7-6(7) 7-6(2)
7-Guillermo Garcia-Lopez (Spain) beat Paolo Lorenzi (Italy) 3-6 7-5 6-4