Carlo Ancelotti's side had conceded just once at home in the league since the start of the season but suffered a day of defensive mishaps as Everton striker Louis Saha earned a surprise point for the visitors.
Didier Drogba's double had looked like extending Chelsea's perfect home record but they were left shaking their heads after a fourth match without a victory in all competitions.
Champions Manchester United are breathing right down their necks and can draw level on 37 points later when they host Aston Villa.
Tottenham Hotspur spurned the chance to move into third spot above Arsenal, losing 1-0 at home to Wolverhampton Wanderers, their first home defeat by the Midlands club since 1973. Arsenal, who are nine points behind Chelsea with two games in hand, face Liverpool at Anfield on Sunday.
Sixth-placed Manchester City trailed three times at Bolton Wanderers but scraped a 3-3 draw, one of six in the Premier League on Saturday.
West Ham United fell into the relegation zone, losing 1-0 to Birmingham City while Sunderland conceded late on in a 1-1 draw at home to bottom club Portsmouth, whose goalscorer Younes Kaboul was sent off for his celebrations.
Honduran Maynor Figueroa scored a contender for goal of the season in Wigan Athletic's 2-2 draw at Stoke City, Hull City drew 0-0 with Blackburn Rovers and Burnley were held 1-1 at home by Fulham.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks