Zola curled home a typical free-kick after 38 minutes after the skipper had capped a fine passage of play with the opener 20 minutes earlier.
But this was a fine display after we lost Robbie Keane and Dean Richards to injury beforehand and then Anthony Gardner midway through the first half with a hamstring injury.
The middle phase of the first half saw us produce, arguably, taking into consideration the opposition, our best football of the season.
In that spell we managed to take the lead and forced Carlo Cudicini into two excellent saves.
Sheringham ran the show as he dropped off Marcel Desailly and John Terry with the right-hand side of Simon Davies and Steve Carr always a threat and Darren Anderton joining in to good effect down the left side.
After a bright start and a couple of half-chances at either end, Davies' ability to break from deep almost led to an opening after 13 minutes but Cudicini was out to sweep up the danger.
The pair came face-to-face two minutes later though as Iversen's precise pass found the midfielder in space in the box. Davies controlled and composed himself but Cudicini was up to the task, blocking to his right from close range.
However, the move never really petered out and seconds later, Davies whipped in a cross from the right that travelled all the way to Anderton at the far post, he drove the ball across goal where Sheringham slid home from close range. A deserved lead.
Chelsea, always capable of creating chances, hit back and forced Davies and Carr to block well from close range.
But the next save again belonged to Cudicini, this time right out of the top drawer, at full length to tip Poyet's drive aside after Sheringham and Anderton carved out the opening.
The home side almost levelled on the half-hour when first Kasey Keller denied Frank Lampard and Mauricio Taricco somehow cleared away from Zola three yards out but then a huge blow as the impressive Gardner limped out of the action with a hamstring problem. Gary Doherty, a striking deputy for Keane in midweek, put on his defensive hat this time.
Unfortunately, the equaliser soon followed. Davies and Zenden came together as Davies attempted to break but was called up for a shove, Zola planted the ball down and curled home the free-kick into the top corner, 38 minutes on the clock.
With the game on a knife edge, the second half unsurprisingly failed to match the first in terms of chances created.
Chelsea had the greater share but King and Doherty stood firm and Keller responded when called upon.
Gudjohnsen almost flicked Lampard's volley towards goal and Keller stood firm to block from the Icelandic striker after he had a clear sight of goal from Petit's pass.
Gronkjaer, a threat down the right, then teed up Zola in the area only for the Italian to fluff his lines from 15 yards.
Keller was there again as Gudjohnsen's shot was deflected but even the arrival of Jimmy-Floyd Hasselbaink failed to jolt Chelsea into any sustained period of pressure.
Carr, always available down the right, broke onto Anderton's pass but couldn't find Sheringham and then, in the last minute, the skipper combined with Poyet to set up substitute Matty Etherington but Cudicini was there again to block.
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4mins: Bright start but first effort on goal from Zenden, shot deflected for corner.
5mins: CHANCE/SAVE. Low cross from Gronkjaer, Zola near post flick blocked by King, Zola onto loose ball but effort saved by Keller.
10mins: Decent move, Anderton cross from left headed wide by Iversen, 16 yards out.
11mins: Zola spun away from marker and fired wide from 25 yards.
13mins: Davies sublime control and almost onto Carr's through ball, Cudicini out of area to clear.
15mins: CHANCE/SAVE. Iversen pass found Davies clear in box, had time to control and pick spot but Cudicini equal to it, Bunjevcevic played ball back to Sheringham, effort blocked by Desailly.
16mins: GOAL. From same possession, deep ball knocked into box found Anderton in space left side of area, drove ball across and Sheringham on hand to slide over the line. 1-0.
19mins: YELLOW. Taricco for block on Gronkjaer.
20mins: Ball across box fell to Zenden, left side, but Davies did enough to take power off shot.
21mins: YELLOW. Petit for foul on Carr.
26mins: Carr blocked Zola's effort as Gronkjaer's cross fell at Italian's feet five yards out.
28mins: SAVE. Sheringham and Anderton set up Poyet's fierce drive from 20 yards but Cudicini there again at full stretch to tip aside.
30mins: SAVE/OFF LINE. Lampard shot saved well by Keller low to his left, Zenden onto rebound, squared across goal where Taricco somehow stopped Zola from tapping home and King hacked away.
36mins: INJURY/SUB. Doherty for Gardner, who looked to suffer hamstring problem.
38mins: GOAL. From questionable free-kick, Zola curled the ball into the top right corner from left angle of box. 1-1.
41mins: Lampard shot straight at Keller.
44mins: Lovely pass from Poyet released Iversen into area, didn't get enough on attempted lob.
Half-time: Chelsea 1-1 Spurs
Half-time: SUB. Melchiot for Zenden.
52mins: Gudjohnsen, on the ground, almost flicked Lampard's volley towards goal, but ball went inches wide.
54mins: CHANCE/SAVE. Keller stood strong to block from Gudjohnsen, clear in box from Petit's pass, King there to tidy up.
59mins: Zola's volley from 20 yards dipped over.
68mins: CHANCE. Gronkjaer beat two players, squared to Zola who fluffed shot from 15 yards.
70mins: SAVE. Keller alert to his left to divert deflected Gudjohnsen shot, Melchiot flew in for rebound but Taricco did enough.
71mins: SUB. Hasselbaink for Le Saux.
76mins: Great switch of play from Anderton found Carr bursting into box, turned Gallas but couldn't find Sheringham with cutback.
Line-ups: Chelsea: Cudicini, Desailly, Lampard, Zenden (Melchiot, 45), Gallas, Le Saux (Hasselbaink, 71), Petit, Gudjohnsen, Zola, Terry, Gronkjaer. Subs: De Goey, Morris, Cole.
Spurs: Keller, Carr, Taricco, King, Gardner (Doherty, 36), Bunjevcevic, Anderton, Poyet, Davies, Sheringham, Iversen. Subs: Sullivan, Freund, Acimovic, Etherington.
A moment of magic from Gianfranco Zola cancelled out Teddy Sheringham's opener as we gained a much-deserved point at Stamford Bridge.