It was Everton's 16th successive game at Villa Park without a win and only the sixth point they have collected on their visit to the Birmingham club.
Both teams recorded their second successive goalless draw in a dour game which failed dismally to hit any heights.
Wayne Rooney was given a rare start by manager David Moyes but the teenager had an ineffective game despite Villa being forced to play veteran striker Dion Dublin as a stand-in central defender.
Rooney was very subdued but the general play of both teams was a fair reflection of their current lowly league positions.
The youngster wasted a glorious chance to obtain his second goal of the season early in the second half.
Kevin Kilbane produced a perfect pass into the middle, but Rooney was agonisingly just late arriving to make a connection only a few yards away from Villa's goal.
Everton had their best chances in the first half when Kevin Campbell glided a header from Thomas Gravesen's corner against the woodwork and later the striker shot over from a Kilbane pass.
Villa's response was a powerful shot from their up and coming young winger, Peter Whittingham, which hit the base of the post.
Their was more urgency about Villa in the second period following the introduction of Thomas Hitzlsperger, but Villa could not capitalise upon the German's powerful play.
Rooney could have capped his return with a second-half goal, but he agonisingly arrived just too late to make contact with Kilbane's low cross.
Aston Villa: Sorensen, Mellberg, Dublin, Samuel, Delaney, Kinsella (Hitzlsperger 45), McCann, Barry (De la Cruz 81), Whittingham, Angel, Vassell. Subs Not Used: Postma, Allback, Ridgewell.
Everton: Martyn, Hibbert, Weir, Yobo, Naysmith, Gravesen, Li Tie (Stubbs 80), Linderoth, Kilbane, Campbell (Ferguson 70), Rooney. Subs Not Used: Wright, Jeffers, McFadden.
Attendance: 36,146
Referee: A D'Urso (Essex).