Toffees topple Chelsea in latest title race twist
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 half-time 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 February 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.
Arsenal manager Arsene Wenger refused to rule his team out of contention for the title when he told Sky Sports News: "It was a massive win for us after the last two disappointments against Manchester United and Chelsea.
"We showed great solidarity against a very well organised team. It was a very tight game but we scored a very good goal and are still in the title race - why not ?" he said.
On balance it turned out to be a better night for Manchester United than they might have expected after going behind against Villa when Carlos Cuellar headed home after 19 minutes.
United equalised four minutes later when Nani's cross from the right was volleyed back across goal by Ryan Giggs. The ball hit the right knee of James Collins and flew past Brad Friedel to give United their 10th own goal of the season.
United manager Alex Ferguson told Sky Sports: "We should have won the game, we were the better team - and with 10 men for a very long time, we still tried to get a result. The players were brilliant."
Tottenham Hotspur lost 1-0 to Wolverhampton Wanderers at Molineux. David Jones scored the only goal after 27 minutes as Wolves moved out of the relegation zone while Spurs stayed sixth on 43 points.
West Ham United also moved out of the bottom three following their 2-0 win over Birmingham City whose former owners David Sullivan and David Gold celebrated their first win since taking control at Upton Park.
Hull City lost 1-0 at Blackburn Rovers, slipping from 15th to 17th, just a point above the relegation zone.