Werder Bremen thumped Hannover 96 3-0 in the day's other game with Claudio Pizarro, Sebastian Prodl and Markus Rosenberg sharing the goals.
Schalke's win kept them fourth, which would earn a place in the Champions League qualifying round next season, with 47 points, and moved them within one point of third-placed Borussia Monchengladbach and a potential place in the group stage.
Borussia Dortmund, held 0-0 at Augsburg on Saturday, lead with 56 points, five ahead of Bayern Munich who thumped Hoffenheim 7-1.
Hamburg, who have won only twice in eight outings since the winter break, are 14th with 27 points, only three ahead of Hertha Berlin in the relegation play-off spot.
Schalke effectively wrapped up victory by scoring three times in the opening half-hour.
Teemu Pukki headed in on five minutes after Atsuto Uchida pulled the ball back from the by-line and Hamburg's defenders stood and watched.
Christoph Melder fired in from close range at a corner in the 26th minute and Klaas-Jan Huntelaar won and converted a penalty after 33 minutes, the Dutchman's 19th Bundesliga goal of the season.
Gojko Kacar pulled one back just before half-time but it proved to be nothing more than a consolation.
"Hamburg played better than us but we took our chances," Schalke coach Huub Stevens said.
"We can't afford to defend like that," said Hamburg's Thorsten Fink.
Hannover had the better of the opening stages against Bremen until Peru striker Pizarro swept home from close range following a set piece for his 16th goal of the season.
Prodl headed in the second four minutes after the restart and Pizarro set up the third for Rosenberg just before the hour.
