The result left sixth-placed Chelsea four points adrift of both fourth-placed Tottenham Hotspur, who won 4-1 away to Bolton Wanderers on Wednesday, and Newcastle, who trail Spurs on goal difference alone, with just two Premier League games of the season left.
Usually, the top three clubs in the Premier League qualify for the Champions League proper, with the fourth-placed side entering the preliminary round. But if Chelsea beat Bayern Munich in the Champions League final at the German club's home ground on May 19, they will take the place that would otherwise go to the team finishing fourth.
Senegal forward Cisse unleashed a powerful shot past Petr Cech to give the Magpies a 19th minute lead. But in stoppage time at the end of the game Cisse topped that effort with a stunning, swerving shot from wide out on the left for one of the goals of this or any other season.
The loss meant Chelsea, like fellow FA Cup finalists Liverpool, suffered a defeat in their final match before Saturday's showpiece match at Wembley.
Meanwhile Spurs won away from home for the first time in 2012 as they moved to within a point of third-placed north London rivals Arsenal just a day after Tottenham manager Harry Redknapp was overlooked for the England job in favour of Roy Hodgson.
At the Reebok Stadium not even the presence in the stands of Bolton midfielder Fabrice Muamba, making his first visit to the ground since suffering a cardiac arrest when Wanderers played Spurs in an FA Cup tie at White Hart Lane on March 17, could inspire his team-mates.
Luka Modric's 25-yard swerving shot put Tottenham in front eight minutes before half-time. Nigel Reo-Cooker gave Muamba and the Bolton faithful something to cheer with a 51st minute equaliser.
But three goals in nine minutes, including two from Emmanuel Adebayor, turned the tide in Tottenham's favour. Rafael van der Vaart scored from Gareth Bale's cross on the hour and two minutes later Adebayor made it 3-1.
Bale then turned provider for the unmarked Adebayor, who rounded Bolton keeper Adam Bogdan, before slotting home his second goal and leaves Bolton in the bottom three level with fourth from bottom QPR but with a worse goal difference.