Top seed Federer impresses while sporting his new, larger racquet and wasn’t particularly troubled by the unseeded Czech.
The Swiss maestro hit seven aces and won 71 per cent of points on serve, but could only convert 23 per cent of his break points, winning just three of 13 opportunities.
Federer will next face Feliciano Lopez or Florian Mayer as he looks to win the title for the fifth time despite this being his first appearance at the event since 2008.
"I guess it’s to a degree some more getting use to, just to see how it reacts on every single shot," Federer said.
"Clearly it reacts better to some shots. But it's important not to think of it the whole time, not to talk about it all the time, but more just sort of go with it, fight for every point, have the right mindset, be optimistic about playing here now and wanting to achieve a good result and that’s what I'm doing.
"I’m just still looking for the timing and the rhythm here, but the longer I stay in the tournament the more confident I am that I’m going to play better and better as the tournament goes on."
World number 11 and second seed Tommy Haas also cruised into the quarters with a very comfortable 6-2 6-4 win over Argentine Carlos Berlocq.
Home-favourite Haas is aiming to win his hometown title for the first time in 11 appearances and will now face Italy’s Fabio Fognini.
ATP Hamburg round three results
1-Roger Federer (Switzerland) beat Jan Hajek (Czech Republic) 6-4 6-3
2-Tommy Haas (Germany) beat Carlos Berlocq (Argentina) 6-2 6-4
3-Nicolas Almagro (Spain) beat Guillermo Garcia-Lopez (Spain) 6-2 6-3
Federico Delbonis (Argentina) beat Dmitry Tursunov (Russia) 6-4 6-3
14-Fernando Verdasco (Spain) beat 4-Jerzy Janowicz (Poland) 7-5 4-0 (Janowicz retired)
5-Juan Monaco (Argentina) beat 9-Benoit Paire (France) 6-3 2-6 6-2
12-Fabio Fognini (Italy) beat Marcel Granollers (Spain) 6-2 6-4
Florian Mayer (Germany) beat 11-Feliciano Lopez (Spain) 7-6(1) 6-2
ATP Bogota round two results
Matteo Viola (Italy) beat 4-Edouard Roger-Vasselin (France) 6-3 7-5
- Sports & Recreation
- Feliciano Lopez
- Florian Mayer
- Tommy Haas