Gabriel Agbonlahor scored for Villa at Stamford Bridge after Didier Drogba had put Chelsea ahead, denting Chelsea's perfect home record and keeping Villa unbeaten after seven games.
Chelsea leads the standings with 16 points - two more than Bolton, which beat Liverpool 2-0. Manchester United, Portsmouth, Everton and Villa all have 13 points.
"We did everything to win except put the ball in the net," Chelsea manager Jose Mourinho said. "It was not our day."
Arsene Wenger took charge of his first game since passing 10 years as Arsenal manager with a 2-1 win over Charlton. It was Arsenal's fifth consecutive win in all competitions after a shaky start to the season.
"My team is back on track, hungrier than ever and they will certainly be fired up now," Wenger said.
Manchester City drew 1-1 with Everton with an injury-time goal from Micah Richards. Sheffield United beat Middlesbrough 2-1 for its first win of the season to move off the bottom of the table.
Chelsea last dropped points at home on Jan. 22 when it drew 1-1 with Charlton last season.
Drogba scored after three minutes when he tapped in a free kick from Arjen Robben. It was his fourth goal in as many days - he hit a hat trick in Wednesday's 3-1 Champions League win at Levski Sofia - and eighth of the season.
Chelsea's Frank Lampard went close to scoring several times, but was denied by goalkeeper Thomas Sorensen, who also stopped a header from Michael Essien.
Aston Villa leveled in first-half injury time through Agbonlahor, who headed in a pass from Liam Ridgewell.
"Chelsea put us under phenomenal pressure, especially in the last 20 minutes," Villa manager Martin O'Neill said.
The match was the first time that Mourinho and O'Neill had faced each other since 2003. Then, Mourinho was manager of FC Porto, which beat O'Neill's Celtic 3-2 in extra time to win the UEFA Cup final.
Liverpool's poor away form continued at Bolton. The Reds are yet to win away from home this season in the Premier League or Champions League.
Bolton midfielder Gary Speed scored in the 30th minute in the 750th club game of his career after Ivan Campo had tapped him a free kick given when the assistant referee ruled that Liverpool goalkeeper Jose Reina had handled outside the box.
However, TV replays showed that Reina had released the ball inside the area before kicking it.
Liverpool manager Rafa Benitez was furious at the decision.
"It is the first time I have seen such a free kick given in England, but what can you do?" he said. "That incident changed the game because we were in control and playing well."
Campo scored the second in the 51st when his header from a pass from Kevin Davies hit the underside of the crossbar and went over the goal-line before bouncing out.
"Our opportunities were very few, but we have taken them," Bolton manager Sam Allardyce said. "That is crucial in the Premiership and certainly against Liverpool, because we knew we were not going to create many chances.
At the Valley, Robin van Persie scored twice for Arsenal's win.
Charlton took the lead through Darren Bent, who scored in the 21st after taking a cross from Jimmy-Floyd Hasselbaink. Television replays suggested that Hasselbaink was offside.
Van Persie equalized in the 32nd when he was set up by Thierry Henry and Alexander Hleb. He scored his second with a volley from inside the area in the 49th.
"It was a goal of a lifetime," Wenger said. "Technically his movement is perfect, but first I thought the ball would go out and it finished in the top corner."
Everton maintained its unbeaten start to the season but was denied victory by Richards. Everton's Andy Johnson scored his sixth league goal of the season when he volleyed in Phil Neville's cross in the 44th.
Sheffield United moved from bottom to 17th after Phil Jagielka scored from 30 yards (meters) in injury time for the club's first win this season. Middlesbrough striker Aiyegbeni Yakubu had scored in the 49th, 14 minutes after Rob Hulse had hit his third goal of the season.
On Sunday, it's: West Ham vs. Reading; Blackburn vs. Wigan; Manchester United vs. Newcastle and Tottenham vs. Portsmouth. On Monday, Watford hosts Fulham.
In the Football League Championship, Cardiff beat Wolves 4-0 to extend its lead at the top of the standings. Second-place Birmingham drew 1-1 with Leicester. Cardiff has 23 points, with Birmingham on 18, and Preston and Crystal Palace on 17.
Source: Fox Sports 
Linear Mode
