That late drama aside, it was a dour game that will raise questions about both teams' hopes of finishing in the top four.
Tottenham, who have scored nine goals in their 10 Premier League games this season, were unable to convert their first-half control into goals, or even clear chances.
Everton were better after the break and they remain unbeaten at home in the league in 2013.
But their carelessness in possession will have concerned manager Roberto Martinez on a day when both defences proved too strong for the opposing attacks.
The first 45 minutes was a perfect snapshot of Tottenham's lack of attacking punch.
Second-half display pleases Martinez
They were quickly in the ascendency but were mainly limited to efforts from outside the area, despite their dominance of possession.
After Sandro and Andros Townsend tried shots from long range, Soldado glanced a header wide from Aaron Lennon's cross.
Tim Howard punched away a Kyle Walker free-kick and the Everton goalkeeper also held a low drive from Lewis Holtby as the pressure continued.
Leon Osman broke forward from midfield and thumped over from 25 yards as Everton finally had an effort on goal with almost half an hour gone.
Vertonghen, a major attacking threat surging forward from left-back in the first half, felt he should have had a penalty when he went down under pressure from Coleman.
Soldado was wasteful once again when he lifted over the bar from the edge of the box after a slick passing move just before the interval.
Tottenham defender Vlad Chiriches, who impressed in his third Premier League start since joining from Steaua Bucharest in the summer, pulled off a fine block to deny Kevin Mirallas after a quick Everton break shortly after half-time.
Villas-Boas pleased with 'good point'
Ross Barkley, left out for the first time in the league this season, came off the bench soon after the hour mark and just missed the top corner with a powerful long-range effort.
In a reverse of the first-half incident, Coleman went down under apparent contact from Vertonghen in the area but referee Kevin Friend was unmoved.
Howard punched away a curling shot from Gylfi Sigurdsson and the delay after Lloris's injury led to nine minutes being added on.
Spurs went the closest late on, with Christian Eriksen's shot being blocked by Phil Jagielka and Sigurdsson dragging wide.
Everton manager Roberto Martinez:
"In the first half Spurs had the initiative in the game. We were good defensively but we lost the ball too cheaply. In the second half we were completely different, imposed ourselves and forced Spurs to defend in their own half.
"It was a very level game but what I will take from it is our character.
"We found a way to impose ourselves in the second half and both teams tried to win until the last seconds."
Tottenham manager Andre Villas-Boas:
"It was very tight, a good game. We had good moments and a great first half with pressing and good attacking combinations and we should have gone ahead in the first half.
"The second half evened itself out but we still managed to slot in a couple of situations in the second half.
"It is a good point in the end. We could have gone second but, considering Everton's aspirations, it was important to get a point."
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