It looked to be plain sailing for the Royal Blues after Eric Maxim Choupo-Moting opened the scoring but Artur Sobiech restored parity.
Klaas-Jan Huntelaar did put Schalke back in the lead before Alessandro Schöpf came off the bench to seal all three points.
Entertaining first half at the HDI-arena
Hannover had been massively improved under Daniel Stendel and almost got the start that befitted their form. A fast move forward broke down twice before a kind bounce eventually found Felix Klaus, with the midfielder seeing his shot superbly tipped round the post by Ralf Fährmann.
As quickly as the hosts had come forward, Schalke found themselves ahead early on for the second time in as many weeks. A throw-in eventually found Leon Goretzka, who produced a superb cross-field ball to find Eric Maxim Choupo-Moting. The wide-man went through on goal and calmly slotted past Ron-Robert Zieler to open the scoring.
Any joy for the Royal Blues was short-lived and they were soon pegged back; memories of Bayer Leverkusen would have flashed in their minds. A storming run down the left from Noah-Joel Sarenren-Bazee left the Schalke defence trailing in his wake, and a simple cross to Artur Sobiech was tapped into an open net.
Hannover almost had a second when a mazy run from Hiroshi Kiyotake saw the Japanese take aim, only to see his shot zip wide. It would instead be Schalke that took a lead into the break. Leroy Sané and Huntelaar combined brilliantly to see the former feed the Dutchman to sweep home on the stroke of half-time.
Schöpf's strike seals it
The second half had fewer chances than the 45 minutes previous. Sarenren-Bazee fired over the bar from close range for the hosts, before Choupo-Moting was denied by Zieler. Manuel Schmiedebach than smacked a thunderous drive from a corner routine off the upright. The play favoured Hannover, but the Royal Blues would nab a third.
Joel Matip picked the ball up mid-way through the hosts' half and went on an incredible run, showing great control to get past several defenders before going one-on-one with Zieler. Schöpf was on hand to round off a lovely move, and breathe new life into their push for fourth. Now just three points behind Hertha BSC and Borussia Mönchengladbach, this win will have been a massive confidence boost. Hannover, on the other hand, are showing positive signs for an immediate Bundesliga return next year.