The Citizens hopes of the quadruple are still alive, despite Guardiola constantly reminding his players to take one game at a time.
After a fairly uneventful 80 minutes or so, Gundogan finally opened the scoring with a diving header after Virginia’s initial smart save from Laporte.
With Everton throwing all their players forward in search of an equaliser, De Bruyne then doubled the visitors’ lead to confirm City’s FA Cup semi-final place for the third consecutive season.
Down the other end, Richarlison went the closest for the hosts but couldn’t beat Steffen, which is why City run out 2-0 winners at Goodison Park.
Gundogan has arguably been City’s player of the season, so it came as no surprise to see him once again make the difference just when Pep Guardiola needed him most.
Everton boss Carlo Ancelotti had done his best to keep the midfielder quiet, with twin destroyers Andre Gomes and Allan tracking Gundogan’s every move to try to stifle his impact.
But the 30-year-old is having his best-ever season in front of goal and there would be no denying him his 16th goal of such an influential campaign.
In a tight clash, the chance he had been awaiting finally came in the 84th minute, after Aymeric Laporte’s shot had bounced back off the bar. There was never any doubt that Gundogan would be in the right place at the right time to finish off the rebound.
Substitute Kevin De Bruyne added a second in the 90th minute but this was a game that was in the balance for a long, long time. Indeed, it was a reminder of how fine the margins are as City look to pull off a historic quadruple.
They return to league action with a trip to Leicester City before facing Borussia Dortmund in the Champions League.
Everton, who crash out at the quarter-final stage of the cup, remain in pursuit of the European spots in the Premier League and they next host Crystal Palace.