Hyypia's men went 2-0 ahead inside 16 minutes thanks to a double from former Hamburg striker Son Heung-Min, only for Maximilian Beister and Pierre-Michel Lasogga to level things up for the visitors.
Son completed his hat-trick 10 minutes into the second half before Stefan Kiessling and Gonzalo Castro made sure of the points, despite a second from Lasogga.
Hyypia, though, was far from satisfied with his side's showing, criticising his players for a lack of concentration.
"It wasn't really a nice match for me," he said.
"Of course I'm happy that we won this game but as a coach it was hard to sit on the bench and watch what was happening on the pitch.
"We started well, we scored two goals and then we conceded some unnecessary ones. The three goals we conceded were totally unnecessary in my opinion. With a little bit more concentration we could have prevented all of them.
"In many situations, we could have played better. But we have had a tough week with (Eintracht) Braunschweig, Shakhtar Donetsk and now Hamburg, so after last weekend this is a step forward."
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
