Steven Pienaar was one of Everton's more industrious players
Everton keeper Tim Howard set a new club record of 16 clean sheets in a disappointing match in which neither side had many threats on goal.
Spurs full-back Gareth Bale sent a 20-yard free-kick over the bar on 16 minutes before Ledley King blocked Jo's shot following Steven Pienaar's pass.
The second half saw Dan Gosling clatter the woodwork with a drive from the edge of the area on 68 minutes.
And Jermain Defoe went close with a fine shot on the turn a minute later.
While Howard usurped Neville Southall's record of 15 clean league sheets set back in 1996, the USA international and opposite number Heurelho Gomes were rarely tested in a game bereft of genuine goal-scoring chances.
Everton season delights Howard
Everton boss David Moyes made one change from the starting XI which beat Sunderland last week, with teenager Jack Rodwell making only his eighth start of the season in place of Lars Jacobsen, with Phil Neville slotting in at right-back in place of the Dane.
Injuries forced Tottenham boss Harry Redknapp into a tactical switch, opting for a five-man defence with Vedran Corluka joining Ledley King and Jonathan Woodgate at centre-back, while Alan Hutton and Bale patrolled the right and left flanks.
Tom Huddlestone replaced the absent Wilson Palacios in midfield, while Defoe made his first start alongside Robbie Keane since the Irishman re-signed for Spurs in January.
The Goodison pitch, already generously watered prior to kick off, became drenched following a heavy rain burst in the first half, making passing particularly hazardous.
However, despite the slick conditions, both sides managed to string a number of passes but crucially lacked any decisiveness in the final third.
The visitors' best chance of the half fell to Bale, whose left-footed free-kick from the edge of the area just evaded the crossbar on 16 minutes.
Redknapp satisfied with 'fair result'
And a timely intervention from Joleon Lescott prevented Keane from hitting the target from the edge of the area on 23 minutes.
Everton had their chances, their best coming five minutes before the interval.
The industrious Pienaar fed a pinpoint pass beyond Tottenham's centre-backs for Jo, whose shot from 16 yards was blocked by King as the Brazilian attempted to slide the ball past the onrushing Gomes.
Tim Cahill came closest to opening the scoring in the second half when his 55th-minute half-volley from 20 yards just evaded the right-hand post of Gomes' goal.
The Brazilian keeper almost added another comedy keeping gaffe to his collection minutes later when he spilled a regulation cross from Leighton Baines, only to recover the ball inches from the feet of compatriot Jo.
We could have won - Moyes
With momentum swinging Everton's way, Gosling came closest to breaking the deadlock on 68 minutes when his drive from the edge of the area rebounded off the left-hand post to safety.
It was the young midfielder's last contribution of the match, substituted for Leon Osman while Louis Saha replaced the largely ineffective Jo.
Neither replacement had touched the ball when Defoe fizzed a fine left-footed turn from the edge of the area past Howard's right-hand post on 69 minutes.
With defences firmly on top, neither side managed to create further chances, a draw a fair reflection of a largely uneventful match.
Everton boss David Moyes on Tim Howard's record: "He has been fantastic, Tim Howard is a professional who works very hard at his game.
"But the record is also a compliment for the players in front of him. Good teams start with good platforms at the back and we have that.
"I thought Spurs were very good in the opening 30 minutes, we found it difficult to stay with them. But we pegged it back and the second half we played well and were unfortunate not to win."
Tottenham boss Harry Redknapp: "We dominated the first half, created good opportunities and passed the ball fantastically. But second half they stopped us from playing.
"But I thought it was a fair result, there were not a lot of chances for both sides, neither keeper has had to put out any world-class saves.
"It was interesting to get a chance to see look at players who haven't had played too much this season to see what they could do."
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