A week ago City were five points adrift of Liverpool but took full advantage after Jurgen Klopp’s side could only manage back-to-back draws, moving ahead of the Reds on goal difference albeit having played one game more.
“A few days ago we could have been seven points behind. Now we are top of the league. That is the best advice, the lesson is never give up,” said Guardiola.
“That is a lesson for all athletes. Try to win the games, because life can change immediately.”
Defender Aymeric Laporte met David Silva’s free-kick to head home his fourth goal of the season, putting City in front just before half-time.
Sergio Aguero and Raheem Sterling both spurned decent opportunities to extend City’s lead after the break before Gabriel Jesus sealed victory in stoppage time.
It was far from a vintage display by City, who instead had to show their battling qualities to secure the points and regain the initiative in the title race.
Attention will now switch back to Liverpool, who can return to the summit with victory against Bournemouth on Saturday, 24 hours before City host Chelsea at Etihad Stadium.
Everton stay ninth after suffering a fourth defeat in five Premier League games at Goodison Park, though they should take some encouragement from a resilient display that was a notable improvement on their performances in recent weeks.
Just seven days ago, Manchester City faced the prospect of falling seven points behind leaders Liverpool after slipping to a fourth Premier League defeat of the season against Newcastle the previous evening.
Klopp’s side missed that opportunity after drawing with Leicester, and a further draw at West Ham on Monday opened the door for City to return to the top for the first time in almost seven weeks.
Guardiola’s side appeared determined to make an impression at Goodison Park, creating three good chances in the opening 20 minutes, with Leroy Sane and Laporte going close before Ilkay Gundogan hit the bar.
City faded after that bright opening but made the breakthrough as half-time approached. David Silva’s free-kick from the left-hand side of the penalty area was headed in by the unmarked Laporte for his first Premier League goal since August.
Aguero and Sterling missed further chances after the break to ensure a nervy finish, though Everton, despite all their effort, failed to truly test Ederson in the Manchester City goal.
Victory was sealed seconds from full-time – Jesus heading home at the second attempt after Jordan Pickford had done well to block his initial shot.
The result puts further pressure on Liverpool who, after a near-flawless campaign so far, have started to show signs of fallibility in recent weeks as they chase a first league title for 29 years.
Three successive league victories have also pushed Tottenham back in contention. Mauricio Pochettino’s side are just five points behind the top two and still have to visit Anfield and Etihad Stadium before the end of the season.
