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The Blues dominated for long periods but looked to be heading for a frustrating draw after Charlie Daniels’ early thunderbolt was cancelled out by Gabriel Jesus’ neat finish.
But Raheem Sterling bagged a 97th-minute winner to send the away fans into a frenzy and maintain City’s unbeaten start to the season.
“Winning in the last minute is always special,” he said.
“It was a tough game, it is always complicated against Bournemouth. They play long balls, balls into the channels and play set-pieces but we got into the game.
“We tried, our finishing was not good but we are there.
“Very happy for the victory. Bournemouth were better in the first 10-20 minutes before Daniels goal, which was outstanding.
“After they scored we started to play and we created chances to score one maybe two goals.
“The second half we started slow but still controlled the game and tried to attack against eleven players defending."
The win leaves City with seven points from their first three games of the new Premier League season after the opening-day win over Brighton was followed up by a home draw with Everton.
The win at Bournemouth moved City top of the Premier League tempoarraily – but Guardiola isn’t getting carried away.
“It is a decent start,” Guardiola said.
“We would prefer nine points but the Premier League is tough, home and away.
“Today it was tough just like it was against Everton.
“On Monday we deserved a point and today we deserved similar if not more so we have points what we deserve so far.”