But victory only came after Connor Wickham had equalised and threatened to condemn the Blues to a fourth 1-1 draw from their last five games.
Guardiola’s side have drawn their three most recent home games by that scoreline despite dominating each match, and while the Catalan was impressed with the spirit shown to win a difficult away game in south London, there was a sense of frustration that his team have dropped points while playing well but won while playing badly.
“Football is something… I said to my players, the frustration for coaches is to discover the secrets of this game," he said. "Sometimes it’s so difficult because you think about playing at home - against Everton, Southampton and Middlesbrough we played better and we are not able to win.
“I want to be honest with you, in that way we are going to be far away, in that way we are not going to win the titles, in the way we played.
“The players know that because they play really, really good [before] and they know that playing that way we can achieve our targets. So we cannot forget that a few weeks ago we [beat] the best team in Europe (Barcelona), but there are games during the season, like [here] after the international break, that you are not brilliant.
“We spoke about that at half-time: we are not brilliant and in the second half we will not be brilliant.”
He returned to the theme later in his press conference and said he preferred the performances against Everton and Middlesbrough, and even part of the comprehensive 2-0 defeat at Tottenham, to the game at Palace, even if he does value the result and the determination required to deliver it.
“[Saturday] was possibly a good step, but in the long term you have to play better,” he added. “Sometimes it can happen once, but when it happens often, in the end you are going to lose.
“I am more satisfied when we play against Middlesbrough, against Everton, even Tottenham the second half, but you have to win.
“That's why it's a huge compliment to the team - maybe more than ever - because we have to win these kind of games and we did it.”