Spurs thought they could have had a last-gasp penalty when Jermain Defoe was challenged by Stiliyan Petrov - but it remained goalless.
It means Liverpool have edged Harry Redknapp's side out of the Champions League places to give the top of the league a familiar look.
Both these teams are naturally attacking and it made for an end-to-end clash at times, with the hosts piling on pressure and Villa looking to counter-attack.
It is no surprise Spurs boss Redknapp expects the race for fourth to go to the wire. He and Martin O'Neill headed into the evening clash encouraged by Manchester City's defeat at Hull and aware of Liverpool's momentum after edging past rivals Everton.
Friedel was the busier of the two goalkeepers in the first half, starting when Luka Modric threaded the ball through Carlos Cuellar's legs for Peter Crouch. Helped by Richard Dunne's block, Friedel managed to save.
The American also parried a fierce 25-yard drive from Tom Huddlestone but saved his best until just before the interval when David Bentley sent over a free-kick and King prodded Crouch's flick towards the top corner. Friedel leapt to his right to get a glove on the ball, with Defoe sending the rebound over.
The visitors had attacks of their own, with Dunne almost on the end of Stewart Downing's cross followed by a penalty shout when Michael Dawson accidentally touched Gabriel Agbonlahor's shot.
Their best chance of the first half came when James Milner's long-range effort was saved by Heurelho Gomes and the Brazilian got up sharply to deny Agbonlahor following up.
Villa were forced into a change, however, midway through the opening period. Emile Heskey was hurt by an earlier Wilson Palacios challenge and headed straight down the tunnel when he was replaced by John Carew, who himself had just returned from a knee injury.
Carew had to adjust to the pace of a pacy encounter with last-ditch tackles and important saves around every corner.
Modric was looking to drift in from the left to influence the game, King had to time challenges perfectly and both sides were threatening from set-pieces.
The start of the second period followed the same pattern, with plenty of attacking football without an end product to break the deadlock.
Friedel was following in the footsteps of Boaz Myhill, Casper Ankergren and Joe Lewis - who all impressed at Spurs' ground in the last month - with his performance between the sticks.
The veteran's next save was from Huddlestone, who fizzed a drive towards the top corner but saw his effort turned around the post.
Carew had sight of goal when he was found at the near post but he could not steer his finish past Gomes.
In the latter stages Dunne blocked a long-range effort from Bentley and Crouch had an effort deflected just wide.
The hosts also had a late penalty shout turned down by Chris Foy when Defoe went over following a challenge by Petrov, before Crouch backheeled wide from close range in stoppage-time.