The Australian won his second-round match against Italy's Andreas Seppi 6-4, 6-4 in one hour and 20 minutes.
With Wimbledon starting in 10 days' time, former world number one Hewitt admitted he was glad to have got a hard-fought match under his belt.
"This match was good, though it was a tough battle for me," the 30-year-old Hewitt said.
"Seppi had already played well against quality players. I remember him playing very well against James Blake at Wimbledon, so I know he plays well on grass.
"I was able to keep the ball flat and I am a little surprised about my performance.
"I feel pretty comfortable playing out there. Every time I come back from injuries, I noticed my ball-striking always comes back quickly and easily.
"It is the adjustment and the feeling for the court that is the thing missing."
Germany's Kohlschreiber awaits in the last eight clash after he enjoyed a 6-3, 7-6 (7-5) victory over seventh-seeded Ukrainian Alexandr Dolgopolov.
"Obviously Kohlschreiber is a quality player, who has come far in this tournament so I have to watch out," said Hewitt, who is also still involved in the doubles.
"I'd like to execute my game like I did today, that would be great."
French third-seed Gael Monfils is also into the quarter-finals and faces another German opponent in sixth-seed Florian Mayer.
The 24-year-old Monfils saw off Croatia's Ivan Dodig 6-2, 6-3, but admitted he is not a natural on grass and was looking to improve his game ahead of Wimbledon.
"I really feel good, especially because I moved well," said Monfils, who beat compatriot Florent Serra in straight sets in the first round.
"I am happy about that, because I do have problems adjusting to grass. In the last 10 days before Wimbledon, I want to improve my overall game further still - serve faster and stronger and work on my movement.
"Last year, I was terrible on grass, because that surface does not come natural to me, so this year I am happy, I want to continue improving.
"All in all, after this second easy win, I think I have made a good debut on grass here in Halle."
Mayer enjoyed a 7-6 (7-4), 3-6, 6-4 win over Taiwan's Lu Yen-Hsun.
He fired down 13 aces on the firm Halle turf which is favouring the big hitters, but says Monfils starts as favourite in their quarter-final.
"In my opinion, Monfils is slighty ahead as the favourite," Mayer said.
"I'm surprised how well he is playing on court here, but I must play my own game and let form on the day decide.
"I will have to get things right under pressure and play my game, otherwise it will be really difficult."
In the other quarter-finals, Germany's Philipp Petzschner will play Canada's rising star Milos Raonic and top seed Tomas Berdych will play fifth seed Viktor Troicki of Serbia.
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