Second-placed Manchester United drew 1-1 at Aston Villa while Arsenal stayed in the hunt after beating Liverpool 1-0.
Saha, who scored against Chelsea in the FA Cup final last season and in the 3-3 draw against them in December, cancelled out Florent Malouda’s 17th minute opener for Chelsea with a header in the 33rd.
He then had a penalty saved by Chelsea goalkeeper Petr Cech on the stroke of halftime before scoring the winner after 75 minutes when he chested the ball down, turned and fired home.
That sent Chelsea to their first defeat in 11 matches and gave Everton manager David Moyes his first victory over the London side on the night he celebrated his 300th Premier League game.
Chelsea remain top with 58 points, but are just one point ahead of Manchester United, who drew at Villa despite playing for more than an hour with 10 men after Nani was sent off for a ragged two-footed challenge on Stilian Petrov.
Nani will now be suspended from the League Cup final against Villa at Wembley Stadium on Feb. 28.
Arsenal ended a run of four league and cup matches without a win beating Liverpool 1-0 at the Emirates where Abou Diaby headed the only goal 18 minutes from time.
They are third on 52 points and Liverpool are fourth on 44.
