Visiting keeper Maik Taylor was rightly red carded for upending Simon Davies in the first half before incredibly Darren Anderton followed in the second half for two yellow cards in the space of four minutes - the second, for a trip, appeared somewhat harsh.
Nevertheless, Fulham's defensive line stuck to their task when they faced 10 against 11 and few chances were created.
To make matters worse, Gus Poyet limped off in the first half and Ledley King tweaked a knee in the final stages.
The first half was a stop-start affair as Fulham took an early lead before being disrupted by two injuries and we struggled to get our passing game going.
Sheringham had an early chance from Anderton's free-kick but headed wide from close range and the lively Poyet nodded over before Fulham's first forced change as Zat Knight replaced Djetou.
But they soon led. Taylor kicked long upfield, Marlet won the aerial challenge and picked up the loose ball, fed Boa Morte whose shot deflected slightly off King and beat Keller.
Marlet then limped off, replaced by Louis Saha and the game lacked any real flow.
Sheringham had appeals for a penalty waved after 27 minutes away as we started to gather some momentum.
Anderton's 30-yard fizzer warmed Taylor's fingertips five minutes later and then the save of the half as Taylor somehow tipped King's towering header onto the underside of the bar before gathering the loose ball.
Poyet limped out of the action after 35 minutes but that low was soon replaced by the high of an equaliser.
The goal stemmed from a bit of trickery from Richards on the half-way line. The big defender jinked past Saha before releasing Davies one-on-one on Taylor, Davies took the ball past the keeper before being brought down - clear penalty and red card for Taylor.
Martin Herrera replaced Taylor as Fulham completed three substitutes and his first job was to pick Sheringham's sweetly struck penalty out of the net.
Fulham, now with two lines of four and Saha as a lone man up front, set out to frustrate defensively in the second half and it worked as chances were few and far between despite all our possession.
Pacy Saha, a threat up front, had the first opportunity of the second half but fired wide under pressure from Keller and King.
It wasn't until the 63rd minute that we carved Fulham open and what a chance. Carr burst down the right and his measured cross picked out Acimovic six yards out only the midfielder to hit the ball against the floor and onto the top of the crossbar.
The Slovenian almost made amends minutes later, latching onto Knight's stumble and lashing his shot inches over with Herrera rooted to the spot.
The growing frustration then took a turn for the worst as Anderton picked up two yellow cards in the space of four minutes and was sent off for what is believed to be the first time in his long career.
That evened things up, lifted Fulham and Saha crashed a shot onto the top of the crossbar.
It took until the final minutes to carve out another opening and it was the old favourite 'Sheringham corner' that almost unlocked the door - this time the skipper's diving header was cleared off the line by Finnan.
MINUTE BY MINUTE GUIDE
2mins: CHANCE. Sheringham headed Anderton free-kick wide from eight yards.
4mins: Poyet late run to meet deep Carr cross but headed wide from 12 yards.
7mins: Malbranque cross found Sava but near-post header no problem for Keller.
12mins: SUB. Knight for injured Djetou.
16mins: GOAL. Long kick by Taylor won by Marlet, he picked up the loose ball and fed Boa Morte who scored despite a strong hand from Keller from the left side of the area. 0-1.
18mins: SUB. Saha for injured Marlet.
20mins: Deep Anderton free-kick found Sheringham at the far post, difficult angle, header straight at Taylor.
27mins: PENALTY? Appeals waved away after Sheringham appeared hauled down by Ouaddou.
32mins: Anderton 30-yarder tipped over by Taylor.
34mins: SAVE. Magnficent Taylor tip onto the underside of the bar from King's towering header.
35mins: SUB. Acimovic for injured Poyet.
37mins: PENALTY/RED CARD. Davies onto Richards pass, through on goal, rounded Taylor who brought him down. Penalty awarded, Taylor off.
38mins: SUB. Herrera for Sava.
39mins: GOAL. Sheringham no mistake from the spot, drilled home to Herrera's left. 1-1.
Half-time: Spurs 1-1 Fulham
46mins: CHANCE. Saha onto Boa Morte's pass, into the box but fired wide under pressure from King and Keller.
49mins: Defence-splitting pass from Bunjevcevic released Carr, he found Acimovic but downward header saved comfortably by Herrera.
53mins: YELLOW. Wome for foul on Davies.
59mins: YELLOW. Richards for foul on Saha.
63mins: CHANCE. Carr burst down the right, squared to Acimovic, six yards out, but hit the ball into the ground, onto the bar and over.
67mins: Doherty header from Anderton cross straight at Herrera.
68mins: YELLOW. Anderton for foul on Boa Morte.
69mins: CLOSE. Acimovic latched onto Knight mistake and lashed his shot inches over with Herrera beaten.
72mins: YELLOW/RED. Anderton second yellow for clipping Saha's heels. Red card.
75mins: WOODWORK. Saha into box, turned onto his left foot, crashed a shot onto the crossbar.
82mins: YELLOW. Boa Morte.
83mins: SUB. Etherington for Acimovic.
89mins: OFF LINE. The 'Sheringham corner' - this time Sheringham's diving header cleared off line by Finnan.
Line-ups: Spurs: Keller, Carr, Taricco, Bunjevcevic, Anderton, Sheringham, Doherty, Poyet (Acimovic, 35; Etherington, 83), King, Davies, Richards. Subs: Sullivan, Thatcher, Toda.
Fulham: Taylor, Finnan, Marlet (Saha, 18), Sava, Boa Morte, Malbranque, Djetou (Knight, 12), Legwinski, Davis, Ouaddou, Wome. Subs: Herrera, Inamoto, Harley.
Fulham's sterling defensive display left us frustrated as both sides ended up with 10 men at the Lane.