In his first match since the epic Roland Garros final where he lost to Carlos Alcaraz Sinner eased past Hanfmann who is ranked 138 in the world.
"I'm very happy. He is a great server and a great baseliner, so breaking him is very difficult on this surface," Sinner said.
"I'm very happy how I handled the tough situations mentally. The first set could have gone into a tiebreak and then anything can happen.
"First matches are never easy on grass, and also second and third matches. I think tomorrow I have the day off, which is good, because the body feels different on this surface."
Sinner will next face Alexander Bublik, who won the tournament in 2023 and also faced the Italian in the French Open quarter-finals, and the top seed said he can only expect "the unexpected" against the unpredictable Kazakh entertainer.
"He's a great player, a great talent. A huge talent, actually, and grass is his favourite surface. He beat me here in Halle, he won (the trophy) here in Halle, so it's for sure a place he loves to play," Sinner added.
Earlier, Russian fourth seed Andrey Rublev beat Sebastian Ofner 6-3 6-4 to advance but other top seeds Ugo Humbert and Francisco Cerundolo fell.
Denis Shapovalov knocked out sixth seed Humbert 6-4 4-6 7-6 (7-4) while American Alex Michelsen beat fifth seed Cerundolo 2-6 7-5 6-4.
Shapovalov's Canadian compatriot Felix Auger-Aliassime also advanced but not before he was taken the distance by Laslo Djere in a 6-3 6-7 (6-8) 6-1 victory.
