A crowd of 22, 352 saw Steffen Iversen give Spurs and early lead, only to be cancelled out by a Shaun Maloney free kick near the half hour mark.
The second period was goalless but not without endevour and both sides had chances to win the game, with Teddy Sheringham missing perhaps the best.
Celtic started the brighter and after only 40 seconds Keller was watching the ball come back off his crossbar following a Healy header.
Spurs then settled and managed to establish a foothold in the game. Carr flashed a shot over after a neat headed set up by Sheringham before we took the lead on nine minutes.
Ziege whipped one of his devilish free-kicks over from the left that found the chest of Iversen in the centre of the Celtic area. The Norwegian chested down before prodding the ball past Hedman in the Celtic goal.
An Anderton free-kick from a similar position minutes later also caused mayhem but without the end result.
Sadly, Ziege was replaced by Taricco after on 17 minutes with the German evidently struggling with an ankle injury.
Just over ten minutes later Celtic were level. Jamie Smith made a charge towards the Spurs penalty area and was up-ended by Taricco. Referee Mr Gallagher awarded a free-kick on the edge of the box and Maloney stepped up and fired a superp strike past Keller's outstretched left hand.
Both teams continued in a lively manner in the minutes leading up to half time but neither goalkeeper was particularly troubled. Sheringham set up Davies for a potshot but a massive deflection steered the ball away from danger.
Five minutes before the break a Taricco cross from the right found Iversen, but the goalscorer could not direct his header and the ball went over.
The second period began with a feisty feel to it a both sides attempted to secure the momentum. Davies, in particular, was speedy in the attack and tenacious in the tackle.
Smart work by Smith and Maloney nearly had Spurs in trouble on 53 minutes. Straight after this Spurs so nearly took the lead when a Sheringham scorcher was saved low to his right by Hedman, who could not hold on to the ball. Acimovic pounced on the rebound and jinked around Hedman, appearing to be felled - Mr Gallagher waved play on.
The tempo of the game cranked up a couple of notches and Maloney caused more problems with his darting runs. Iversen was just caught offside when bearing down on goal following a sweet ball from Acimovic.
Keller was next called into action to make a smart low save from substitute Petrov after 68 minutes. Shortly afterwards Celtic had a good call for a penalty when Fernandez went to ground but, again, Mr Gallagher was not to be moved despite howls from the big Celtic support.
Gary Doherty joined the attack on 72 minutes as a replacement for Acimovic, slotting in alongside Iversen with Sheringham dropping off.
But it was Sheringham to the fore a few minutes later when he met a wonderfully flighted cross from Iversen. The skipper flicked his head, but directed his effort onto Hedman's left hand post.
A Taricco curler was fielded by Hedman on 82 minutes before Sylla gave Keller a scare with a low drive that sped wide. Sheringham was then just wide with a header from another Iversen cross. With three minutes remaining Teddy was clean through but failed to navigate a route past Hedman.
Spurs: Keller, Carr, Bunjevcevic, Davies, Perry, Richards, Anderton, Acimovic (Doherty 71), Iversen, Sheringham, Ziege (Taricco 17). Subs: Taricco, Sullivan, Doherty, Ricketts, Etherington, Rebrov, Bortolozzo, Blondel.
Celtic: Hedman, McNamara, Valgaeren (Boyd 53), Healy (Miller 83), Maloney (Sylla 72), Smith (Petta 76), Crainey (Balde 55), Guppy, Fernandez, Laursen, Lennon (Petrov 45). Subs: Douglas, Boyd, Sylla, Balde, Miller, Petta, Petrov.
It finished all square at the Lane in a lively pre-season encounter between Spurs and Scottish champions Celtic.