Huub Stevens' men scored three first-half goals to heap more misery on the visitors, who sit just four points clear of the relegation zone
The hosts took an early lead through Teemu Pukki, before Christoph Metzelder doubled the advantage. Klaas-Jan Huntelaar added a third from the spot, before Gojko Kacar pulled one back.
Schalke were forced to play a portion on Thursday's Europa League loss to Twente with 10 men, but showed no signs of being ill-affected by their midweek exertions.
It took a matter of seconds for the returning Huntelaar to test Jaroslav Drobny, forcing the Hamburg goalkeeper to dart off his line to claim a threatening cross.
It was not long before the hosts went ahead. Atsuto Uchida found space on the right, and sent in an inch-perfect cross for the unmarked Pukki, who headed past the helpless Drobny with ease.
Scoring such an early goal only managed to rouse Hamburg, who set about trying to find a route back into the contest, with Jacopo Sala sending a well-placed effort just off-target.
Uchida made a stunning tackle to deny Ivo Ilicevic, who had been set up by a cunning dummy from Mladen Petric, Tolgay Arslan played in the advanced Marcell Jansen, who blasted a shot into the side-netting.
Both Hamburg full-backs were eager to aid their attacking colleagues, and Dennis Diekmeier's cross found Arslan, whose volley was well saved by Timo Hildebrand.
As the visitors poured men forward, however, they left themselves susceptible to counter-attacks. Huntelaar played in Jermaine Jones, who was denied by Drobny when he should have done better.
The American's miss was to matter little, however. Jose Manuel Jurado launched in the resulting corner, finding Metzelder, who had time to chest the ball down before blasting it home, despite Drobny's best efforts.
Trailing by two goals did nothing to dampen the visitors' impetus, though. Kacar lined up an effort from distance, forcing Hildebrand into an impressive save, but they were to be stung on the break yet again.
Pukki won a corner with a low drive that took a flick off Drobny's outstretched boot, and Heiko Westermann was adjudged to have fouled Huntelaar as the duo jockeyed for position. The Dutchman stepped up to take the resulting penalty, and made no mistake.
The third goal initially left the visitors bewildered, and Schalke had the chance to extend their lead, with Drobny making another impressive save from a Pukki volley.
A defensive error, however, gave the visitors a path back into the match. A poor clearance from Joel Matip went straight to Kacar, who volleyed the ball expertly past Hildebrand with the last kick of the first period.
The second half started in a far more static manner, with Schalke seeming wary of making the same sort of mistake that allowed Hamburg back into the match, and the visitors eager not to commit too many bodies forward, as they had done before the break.
A great ball by Jansen set up Petric, but the Croatian's cross was aimless, and failed to find a Hamburg body when he should have done better.
Gokhan Tore's introduction provided a direct outlet for Hamburg, with the young Turk testing Hildebrand from distance and sending in some threatening crosses that were cleared by the Schalke back line.
At the other end, an audacious attempt from Jurado was well-held by Drobny, before Jones headed a corner from the Spaniard over, before Raul managed to clear the bar from a matter of yards after an impressive run from Uchida.
A winding run from Tore set up Petric, who was denied by a great block by Matip. The Cameroonian recovered to shepherd the follow up out of play.
In the end, the first half salvo was enough for Schalke to close the gap on Borussia Monchengladbach to a mere point, Hamburg meanwhile, slip into 14th, a worrying four points above Hertha Berlin.
Meanwhile, in Sunday's early kick-off, Werder Bremen saw off the challenge of Hannover, claiming a 3-0 victory at the Weser Stadion to open up a four-point gap between themselves and their opponents.
The visitors squandered a number of first-half chances, and were duly punished by Bremen, who took the lead through Claudio Pizarro. Sebastian Prodl headed in a Mehmet Ekici set-piece shortly after the break, before Markus Rosenberg made it 3-0.