Sidorenko, a lucky loser who was ranked No. 193 coming into the tournament, earned his second victory at the ATP Tour level and has the best career result by making the last eight.
"He has played a lot of matches this week so I suppose he is in very good shape and I have to watch out and play my best tennis," Hanescu said.
The Romanian dominated his match against Schuettler, who double-faulted to give away the first set.
"I really played very well. My game was at maximum level. I played my best shots," Hanescu said. "He played solid but I was too good today."
In the first round, Paul-Henri Mathieu of France edged Mikhail Youzhny of Russia 7-6 (4), 7-6 (4), beating the 2002 Stuttgart champion for the first time in five matches. Martin Vassallo Arguello of Argentina came from behind to defeat Andrey Golubev of Kazakhstan 3-6, 6-3, 6-0.