After Hamburg took an early lead through striker Michael Gregoritsch, Kiyotake converted a second-half penalty and then provided the cross for the winner.
The attacking midfielder swung the ball in from the right and Senegal defensive midfielder Salif Sane powered home his header on 67 minutes.
The win lifted Hanover up to 14th and pushed Werder Bremen into the bottom three after their 3-1 defeat at home to Borussia Dortmund on Saturday.
Earlier, VfB Stuttgart also climbed out of the relegation places with a 2-0 win at home to Darmstadt, thanks primarily to an own goal.
Stuttgart climbed up from second from bottom to 15th with their third win in their last six league games after Darmstadt defender Gyoergy Garics headed the ball into his own net on 68 minutes.
It was no more than hosts Stuttgart deserved, just moments after teenage striker Timo Werner had headed against the crossbar.
Werner finally got on the scoresheet with the last kick of the game when he darted behind the defence and rounded the Darmstadt goalkeeper on 94 minutes.
It was the first time in five away matches that mid-table Darmstadt have lost on the road.
On Saturday, second-placed Borussia Dortmund cut the gap behind leaders Bayern Munich to five points as Marco Reus netted twice in Bremen.
Reus fired in the opening and third goals, but Borussia should have won by more as Gabon striker Pierre-Emerick Aubameyang squandered three clear chances.
Right winger Henrikh Mkhitaryan capped a superb display with Dortmund's second having provided the final pass for both of Reus' goals.
Wolfsburg climbed to third with a 2-1 win at home to fellow Champions League side Bayer Leverkusen after Nicklas Bendtner scored the opener and Julian Draxler hit the winner.
Ex-Manchester United striker Javier Hernandez equalised for Leverkusen just before the break, but the game was marred by two poor refereeing decisions from Manuel Grafe.
The FIFA-listed referee missed a clear offside for Bendtner's goal, then failed to award a penalty when Wolfsburg's Daniel Caligiuri was fouled by Leverkusen goalkeeper Bernd Leno in the second half.
Borussia Moenchengladbach earned their sixth straight victory to go fifth with a 4-1 win at Hertha Berlin having been bottom in September with five defeats.
Gladbach's caretaker coach Andre Schubert earned his sixth straight league win since taking charge to level the record for a new Bundesliga coach.
The result boosts Gladbach ahead of Tuesday's Champions League match at home to 2015 finalists Juventus while Hertha drop to sixth.
Gladbach are now just two points behind fourth-placed Schalke, who needed a late Leroy Sane equaliser in their 1-1 draw at home to Ingolstadt after the Bavarian visitors took a shock first-half lead.
Bochum-born Cameroon internationals Joel and Marvin Matip faced each other for the first time with Joel at centre-back for Schalke while Marvin captained Ingolstadt.
Huub Stevens picked up a point in his first game as coach of Hoffenheim in their goalless draw at Cologne.
Caretaker coach Stevens has been tasked with keeping second-from-bottom Hoffenheim up, with 28-year-old Julian Nagelsmann set to make history next season as the Bundesliga's youngest head coach.
Japan's Yoshinori Muto claimed a hat-trick to rescue a dramatic point for mid-table Mainz in their 3-3 draw at bottom side Augsburg.
Having given Mainz a 2-0 lead before Augsburg roared back with three goals, Muto scrambled the ball over the line for the 93rd-minute equaliser.