Chelsea took the lead through Florent Malouda but Saha's 100th goal in English league football levelled proceedings midway through the first half.
The Frenchman then missed a late first-half penalty but he made amends 15 minutes from time, capitalising on a John Terry mistake to volley home.
Despite the point Chelsea, remain top of the table after Manchester United were held at Aston Villa.
After a slow start Chelsea began to turn the screw and with 17 minutes gone Malouda broke the deadlock. The France international latched on to Didier Drogba's flick-on and calmly slotted the ball beyond the helpless Tim Howard from inside the penalty area.
Prior to Malouda's sixth Premier League goal of the season, chances had been few and far between with Frank Lampard dragging a shot wide, while the hosts were strangely off the pace.
The goal failed to spark an Everton comeback and it was the visitors who looked the more likely scorers with Ricardo Carvalho heading a 25th-minute Lampard corner tamely at Howard when unmarked.
But the hosts equalised in the 33rd minute when Saha stole a march on Terry following a Landon Donovan corner and the former Manchester United striker powerfully headed beyond Petr Cech.
Everton dominated the remainder of the half and should have been in front at the interval but Saha saw his penalty brilliantly saved by Cech low to his left after Carvalho had tripped Donovan.
The second half was all action but there were few chances until Saha's 75th-minute strike. Former England captain Terry misjudged a long ball and, as the ball dropped, Saha brought the ball down on his chest before crashing a left-footed volley beyond Cech.
It was all Chelsea from then onwards and minutes later the visitors thought they were level only for Drogba's shot to cannon back off the bar after Everton had failed to deal with Lampard's corner.
It was then the turn of substitutes Salomon Kalou and Daniel Sturridge to go close for Chelsea but Howard was equal to both efforts as the FA Cup holders succumbed to their fourth league defeat of the season.