Bayern Munich top the standings following their 2-1 win over Freiburg on Saturday with Schalke 04 two points adrift in second place after beating VfB Stuttgart by the same score.
Leverkusen's emphatic win put an end to any crisis talks after the team had failed to win their last three matches and had also suffered their first defeat of the season last week against Nuremberg.
"The team really improved in the second half, calmed down and became more accurate and we deserved to win. We reacted very well after the equaliser," Leverkusen coach Jupp Heynckes told reporters.
Kiessling, who has almost certainly booked a place in Germany's World Cup squad with a stunning season so far, gave his team the lead in the 22nd minute, against the run of play, when he broke free and beat keeper Frank Rost with a well-placed low drive.
ERRATIC ADLER
The hosts, without suspended playmaker Toni Kroos, failed to hold on to their lead when Hamburg equalised through former Leverkusen player Ze Roberto in the 33rd, following a blunder by Germany keeper Rene Adler, who failed to clear the ball after colliding with team mate Sami Hyypia.
Adler has been named as the starting Germany keeper but was far from consistent for the third straight game, after errors in Germany's friendly with Argentina and against Nuremberg in the league last week.
Leverkusen, however, regained control and their early second-half pressure paid off when Eren Derdiyok rose to connect with a deep Daniel Schwaab cross to head home his 12th goal of the season in the 55th minute.
Kiessling notched his second of the evening in the 62nd when Renato Augusto crossed from the right and the Germany international shrugged off defender Guy Demel to give his team a two-goal cushion with a diving header.
Hamburg briefly thought they were still in with a fighting chance when David Rozehnal pulled one back from close range in the 83rd but 30 seconds later Gonzalo Castro sealed the win for the hosts with a powerful shot at the edge of the box.
In Sunday's other match, Werder Bremen beat hosts Hoffenheim 1-0 courtesy of Claudio Pizarro's 11th goal of the season, to move up to 42 points, one behind Hamburg who are fifth, and remain in the hunt for a European spot.
