Guardiola’s side were in danger of being blown away by Liverpool in the title race after a damaging defeat at Newcastle last week.
But Liverpool have faltered with successive draws against Leicester and West Ham, allowing City to get back in the hunt.
A hard-fought victory at Goodison Park, secured by goals from Aymeric Laporte and Gabriel Jesus, lifted City above Liverpool on goal difference.
And boss Guardiola insisted City’s return to the summit was a tribute to his players’ refusal to accept they were out of the hunt.
“Goodison Park, 2-0, we have to be happy. In terms of consistency, we didn’t concede one shot on target. To score in the last minute of the first half helped us a lot,” Guardiola said.
“We are not the tallest team in the world so we don’t expect to score from set-pieces, but (assistant coach) Mikel Arteta works a lot on them. I am so satisfied.”
City have now played one more league match than Liverpool because their trip to Everton was a fixture brought forward due to their League Cup final against Chelsea later in February.
So, while City have the advantage for now, Guardiola knows Liverpool can regain pole position if they win their game in hand.
For now, Guardiola is just delighted with the way City have piled the pressure on Liverpool by catching them so quickly.
“We have a game every three days for three months. I don’t know how far we will get, maybe we will die in the road, but we are trying,” Guardiola said.
“We have played one more game than Liverpool. It’s good to be top but Liverpool has a game at Old Trafford.
“I don’t think too much about that but four or five days ago we could have been seven points behind, it is a lesson to never give up.
“We have an incredible test on Sunday against Chelsea.”
