City trail their table-topping neighbours by five points, having played a game more, ahead of Saturday's lunchtime showdown at Old Trafford.
United tasted defeat for the first time this season at Wolves last week and Zabaleta is determined to inflict a first home reverse on Sir Alex Ferguson's side since April last year.
Battle cry: Zabaleta (left) is confident of getting a result at Old Trafford
He said: 'I believe 100 per cent we can win because we show our character when we are in games that we really need to win.
'We know it will be very difficult. United are very strong and are unbeaten at home, so it would be great to break that record.
'Everyone is waiting for Saturday because we know it's one of the best games to play in and enjoy.'
Manchester City sit in third place behind Arsenal after last week's win over West Bromwich got them back on track following a defeat against Aston Villa and a draw with Birmingham.
Argentina full-back Zabaleta, 26, added: 'Before the West Brom game we knew it was a special day for us after losing to Villa and drawing at Birmingham.
'If we are to fight for the title we have to try to win every game. We have 12 games left and have to believe that if we carry on playing as we did on Saturday we have a great chance of being at the top.'
May insists he never meant to taunt City after being forced to cancel eventManchester City race up Europe's rich list, but United remain Premier League's wealthiestLet them boo me! Tevez relishing Old Trafford return as City striker eyes winDe Jong joins team-mate Balotelli as a major doubt for the Manchester derbyAll the latest Manchester City news, features and opinionAll the latest Manchester United news, features and opinion
Explore more:People: Alex Ferguson Places: Birmingham, Argentina