Led by immaculate displays from the likes of Ledley King, Paul Robinson and Noureddine Naybet, we refused to buckle under wave after wave of Chelsea attacks, not least when they turned up the heat in the second half.
However, the best chance of the game fell to Robbie Keane who looked to the skies in disbelief as Chelsea keeper Petr Cech somehow tipped his close-range header over from Simon Davies' cross.
The result means we've won two and drawn four of our six Premiership starts and sit in fifth place.
Davies came back in for Michael Brown with Keane replacing Fredi Kanoute as the other change from last week's goalless draw against Norwich City.
Chelsea always had the edge but came up against a goalkeeper in superb form in Robinson who produced two fine saves to deny Didier Drogba in the first half, both lightning darts off his line to block as the striker burst into the box.
Drogba was centre of most of the home side's attacks but after his overhead kick sailed wide at the start of the second half, our best chance arrived.
We enjoyed decent possession down the right flank, Davies whipped in a cross that evaded Terry and Carvalho and found Keane, 10 yards out and it looked like goal all over until Cech's fingertips diverted the ball over.
That was our last sniff at goal as Chelsea poured forward but clear-cut chances remained at a minimum.
Robinson and King kept out Drogba, Terry flicked Frank Lampard's corner just wide, crossed missed their targets, Drogba volleyed wide again and then Robinson's best save, superb reactions to keep out a Lampard free-kick that went through a crowd of bodies.
Gudjohnsen struck the foot of the post with five minutes left but despite camping in our half and five minutes added time, that was about that.
MINUTE BY MINUTE
1min: King key header away from dangerous Lampard corner.
4mins: Robinson out quickly to deny Drogba breaking into box.
8mins: Lampard 30-yarder flew a yard wide.
20mins: Gudjohnsen burst into the box but King over to cut out danger.
23mins: Cole cross, Gudjohnsen header from 15 yards always wide.
24mins: Atouba to byline but Ferreira cut out cross with Keane and Defoe waiting.
29mins: Robinson comfortable save from Gudjohnsen's volley.
32mins: Naybet fine challenge to deny Drogba but unlucky bounce back to the striker - Robinson out quickly to block follow up.
Half-time: Chelsea 0, Spurs 0
48mins: Drogba overhead kick from Ferreira long throw looked closer than it was.
49mins: YELLOW. King for foul on Drogba.
55mins: SAVE. Our best move yet ended with deep Davies cross met full on by Keane, 10 yards out, amazing save from Cech to tip over.
56mins: Drogba onto through ball, Robinson out quickly, Naybet completed cover.
58mins: Terry flicked Lampard's header just wide.
60mins: Cole away from Naybet, low cross cut out by King.
61mins: Drogba break to byline but didn't give Gudjohnsen or Cole a chance with cross.
65mins: SUBS. Duff and Kezman for Cole and Tiago.
66mins: Cech made a bit of a meal of Redknapp volley, led to more pressure and a couple of corners.
73mins: YELLOW. Redknapp for foul on Terry.
73mins: SUB. Brown for Atouba.
75mins: Drogba onto Gudjohnsen header but got volley all wrong.
77mins: Robinson brave punch with Drogba flying in for header.
79mins: SAVE. Robinson superb reactions to palm out Lampard free-kick that travelled through bodies in box.
83mins: Duff volleyed ball across six-yard line but no-one there to tap in.
84mins: WOODWORK. Gudjohnsen volley from 20 yards hit foot of post.
84mins: SUB. Smertin for Bridge.
86mins: SUB. Kanoute for Defoe.
87mins: Drogba onto long ball in box, bundled past Pamarot but King there to clear.
Injury time: YELLOW. Smertin for foul on Brown.
Line-ups: Chelsea: Cech, Ferreira, Carvalho, Terry, Bridge (Smertin, 85), Makelele, Lampard, Cole (Duff, 65), Tiago (Kezman, 65), Drogba, Gudjohnsen. Subs: Pidgeley, Gallas.
Spurs: Robinson, Pamarot, Naybet, King, Edman, Davies, Redknapp, Mendes, Atouba (Brown, 73), Keane, Defoe (Kanoute, 86). Subs: Keller, Mabizela, Gardner.
Referee: Mike Riley
A superb defensive display kept out Chelsea and maintained our unbeaten start to the Premiership at Stamford Bridge.