A beautiful, long-range strike from Pedro, a Gary Cahill tap-in and a neatly worked goal from substitute Willian secured three points in the trickiest test in Chelsea's title run-in.
While aware of the significance of the victory, the Italian manager, in his first season in the Premier League, remained wary of counting his chickens.
"At this part of the season every win is a great win for us. Before this game there were five games to go. Now there are four games to go. For us every win is a great win and for this reason we must celebrate in the right way, with my players with the staff, with our fans.
"We have to have great enthusiasm and great patience because I think we are having a great season but for it to become a fantastic season we must win," he told reporters.
That 'fantastic season' could yet become a repeat of the club's double -- Premier League and FA Cup -- triumph in 2010 with Conte's team facing Arsenal in the FA Cup final at Wembley on May 27.
Everton was expected to be the toughest game in Chelsea's run-in. Ronald Koeman's team had lost only one game at Goodison before Sunday and had won their last eight in a row but after a tight first half Chelsea ran out comfortable winners.
Read the full article on eurosport.co.uk: Conte wants Chelsea's great season to become "fantastic"