A 17th-minute penalty from Franco Di Santo and Guido Burgstaller's 78th minute goal saw Schalke move on to 23 points, ahead of third-placed RB Leipzig on goal difference.
Argentine striker Di Santo converted his spot kick, awarded for a foul on Yevhen Konoplyanka, for his first league goal since March 2016.
But the hosts were made to sweat with Hamburg hitting the post early in the second half and pushing for an equaliser before Burgstaller settled nerves for Schalke after more good work from Konoplyanka.
Schalke are now unbeaten in their last six games but remain six points behind leaders Bayern Munich, who beat Augsburg 3-0 on Saturday to move on to 29 points, while Leipzig slipped up with a 2-2 draw at Bayer Leverkusen.
Borussia Dortmund slumped to their fourth loss in the last five matches with a 2-1 loss to VfB Stuttgart and have dropped to fifth on 20.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
