An own-goal from Peter Crouch - whose winner at Eastlands a year ago clinched fourth spot for Spurs at their opponents' expense - gave City a 1-0 win and the place among Europe's elite they have craved since the Abu Dhabi takeover in 2008.
It cost Mark Hughes his job as manager and has cast a shadow over Mancini's 17-month reign, but the Italian delivered and can exceed expectations by lifting the FA Cup at Wembley on Saturday.
Manchester City 1 Tottenham 0: Now read Matt Lawton's match report
Wrong end, Peter: Tottenham striker Crouch (left) prods into his own net for the winning goal
City will now play in Europe's premier competition for the first time in 43 years, while the result also means their Wembley opponents Stoke qualify for the Europa League next season.
Mancini acknowleged the significance of his achievement, saying: 'I think it's very important for my job, but first of all I'm happy for the supporters and the people who work at this club.
'This is for them because after many years Manchester City can play in the Champions League.
Hart stopper: City goalkeeper Joe erupts with delight at the final whistle
'When I arrived here I said that City could become one of the top teams in Europe in two or three years. City have everything to do this but we've got it because the players want to play in the Champions League and they deserve to play in the Champions League.
'Yes it's a relief. I'm happy because it was our first target and I have to thank the players because they did a fantastic job.'
Mancini played down a brief touchline spat with Carlos Tevez before the City skipper was sent on in the 83rd minute to prove his fitness ahead of the Cup final following a hamstring injury.
Job well done: Roberto Mancini (right) congratulates the returning Carlos Tevez while City celebrate
Not for the first time this season, Tevez had some angry words for his manager but Mancini said: 'I didn't hear him, I was concentrating on the game. I told him to warm up because he was going on in two minutes but, really, I didn't hear anything.'
Mancini will now wait to decide what role Tevez can play at Wembley but admitted that having to field his strongest line-up could harm City's hopes of lifting their first trophy in 35 years.
Hatt's off: Ricky Hatton was at Eastlands to celebrate Manchester City's win
He added: 'It was difficult to put Carlos on. For 25 minutes of the second half we suffered because Tottenham tried to score a goal, but it was important for him to play for five minutes.
'We have four days. I want to take all the time to decide this. I don't think he can be 100 per cent ready because he only played for 15 minutes and has only had one week with the team. But we have four days, then we need to decide.'
Let's all do the Poznan: City supporters celebrate their team's feat
'It will not be easy for us to recover because we used a lot of energy against Tottenham. It will be a big mistake to think it will be easy against Stoke.'
City's players were able to celebrate after victory gave them an unassailable lead over Liverpool and Spurs with only two games to play.
Hart said: 'This means the world. Trips to Real Madrid, AC Milan and Inter Milan - what more can you ask for?
Credit where it's due: James Milner (second left) is congratulated for setting up the winner
'We now need a trophy and that is this Saturday. We got this tonight and we now need to give these fans a trophy.'
Defender Vincent Kompany called on City to close the two-point gap on Arsenal and snatch third place to avoid a qualifying round this summer.
Kompany said: 'It doesn't mean we are in the Champions League. We would have to qualify so why not get Arsenal? We feel they may drop points and we think we can get six points.'
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Explore more:People: Vincent Kompany, Peter Crouch, Mark Hughes, Carlos Tevez, Roberto Mancini Places: Liverpool, Manchester, Europe