A fourth successive victory also reduced the deficit behind Chelsea to eight points and with 13 league games still to play – and City yet to visit Stamford Bridge – the Blues are hitting form at just the right time.
And the Argentine keeper – who produced two crucial saves in each half – insisted City, who are also in contention for the Champions League and FA Cup, were full of confidence as the season enters its decisive last third.
“We have to win our games. After we see what happens with the rest of the teams but we can only do our job,” said Caballero.
“We fight together. We are really happy today. I have been waiting for this chance for a long time so I always try to do my best for the team.”
City’s man-of-the-match at the Vitality Stadium was winger Raheem Sterling who produced a superb all-round display.
The England star struck the opening goal in the first half and then turned provider after the break for the second which saw Bournemouth’s Tyrone Mings’ put in to his own net under pressure from substitute Sergio Aguero.
The Argentine striker had come on after just 13 minutes following an ankle injury to Gabriel Jesus and Sterling was quick to praise Aguero’s contribution.
“We know Sergio’s ability and it is great to have a player like that in the squad. He is world class,” said Sterling.
“Before the game we knew it would be difficult. Bournemouth play amazing football at times and you saw that today.
“Credit to them they pushed and pushed and luckily we got the two goals. I am always trying to get on the scoresheet, it doesn’t always happen.”
