After their shock defeat by Nuremberg, Leverkusen's win leaves them third in the league, but just two points behind leaders Bayern who needed two goals from winger Arjen Robben to come from behind and beat Freiburg on Saturday.
Kiessling's double makes him the league's top-scorer with 16 goals for the season as he has now scored three goals in two games.
The Germany striker opened the scoring, then produced a powerful header after Swiss striker Eren Derdiyok also scored to put the hosts in control.
Hamburg fought back to 3-2 through goals by Brazil midfielder Ze Roberto and Czech Republic defender David Rozehnal before Leverkusen's Gonzalo Castro settled the tie with his side's fourth goal on 84 minutes.
It was the Peruvian's 11th league goal of the season and showed why Bremen were prepared to pay English giants Chelsea two millions euros for him last August to bring him back from the Premier League.
The result leaves Bremen sixth in the table and one-point from the top five which would qualify them for a place in Europe with eight league games left this season.
"Claudio can be vital in such a game, last Thursday's match clearly took a lot out of us."
On Saturday, Bayern Munich suffered a Champions League hangover before Dutch winger Arjen Robben scored twice to seal a 2-1 win over strugglers Freiburg to put the hosts back on top of the Bundesliga.
Earlier rock-bottom Hertha Berlin slipped closer to relegation after suffering a 2-1 home defeat to fellow strugglers Nuremberg who grabbed an injury-time winner.
Their second straight wins lifts Nuremberg up to 15th and out of the relegation zone.
Dortmund moved up to fourth with a 4-1 victory at Bochum while Wolfsburg claimed their fourth-straight league win under caretaker manager Lorenz-Guenther Koestner when they hammered Moenchengladbach 4-0 to go eighth.
It was Schalke's third successive win and their eighth at home this season while Kuranyi's timely strike was his 14th of the campaign.
Source: AFP Global Edition