The City right-back scored the opening goal before Edin Dzeko and Sergio Aguero netted in the second half to seal the win.
Zabaleta was pleased to see City keep a rare clean sheet while peppering Asmir Begovic’s goal in a one-sided encounter at Eastlands.
“The most important thing is the performance of the team,” he said.
“We had a great game, we had a lot of chances, defensively we were very solid and it’s another clean sheet.
“It’s a good three points. We know we are under pressure. We are seven points behind United and so it’s going to be very tough. Staying positive and keeping working is the key to catching United.”
Roberto Mancini was also satisfied with the victory, especially an improved defensive performance after conceding four goals in their previous games at Norwich City and Sunderland.
“We played very well, like we played against Norwich and Sunderland, but sometimes it’s not enough to play very well, it’s important to score,” said Mancini, whose side remain seven points behind leaders Manchester United.
“In the first half we deserved to score two or three goals, but it was difficult because Stoke is the best defence in the Premier League.
“It was important to keep a clean sheet, because if we start to score and don’t concede a goal we can have a chance to recover these points.”
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