Ignacio Pussetto's goal-line clearance denied Tottenham a last-minute winner at Watford by just 10.04mm in a goalless draw at Vicarage Road.
Pussetto, making his Watford debut as a substitute, slid in to clear Erik Lamela's goalbound effort off the line in the second minute of injury-time and prevent the below-par visitors from stealing a win.
By then the Hornets should have been in front but Paulo Gazzaniga kept out Deeney's 70th-minute spot-kick, awarded for a Jan Vertonghen handball, and they were also left to rue missing a number of other fine chances.
Heung-Min Son was denied by Ben Foster before half-time but, within minutes of the restart, Abdoulaye Doucoure and man-of-the-match Ismaila Sarr wasted glorious opportunities to open the scoring, before Deeney fluffed his lines from 12 yards with 20 minutes to go.
Pussetto's late intervention ensured Tottenham extended their winless league run to a fourth game, while Watford are now unbeaten since December 12 and have taken 14 points from Nigel Pearson's six games in charge.
Watford: Foster (7), Mariappa (6), Dawson (7), Cathcart (7), Masina (6), Doucoure (7), Capoue (7), Sarr (8), Chalobah (7), Deulofeu (7), Deeney (5).
Subs: Pereyra (6), Pussetto (n/a)
Tottenham: Gazzaniga (7), Aurier (7), Alderweireld (6), Vertonghen (5), Tanganga (5), Lo Celso (6), Winks (6), Lamela (5), Alli (6), Son (6), Moura (6).
Subs: Eriksen (7), Fernandes (7).
Man of the match: Ismaila Sarr
How Spurs held on to draw at Watford
The form of these two clubs over the festive period put a markedly different spin on what may have been seen as an easy three points for the visitors only a few weeks ago, but Watford are a different club under Pearson.
From the off they set out to frustrate Tottenham without the ball and hurt them with it, and Gerard Deulofeu should have tested Gazzaniga from one such break, but he fired well wide from 20 yards.
At the other end, Son twice found space on the left but he appeared to have left his shooting boots at Hotspur Way, while Lucas Moura wasted the chance of the half by shooting straight at the onrushing Foster when played through in the box.
Tottenham looked somewhat toothless without talisman Harry Kane and the travelling fans did not clap their side off at the break, but if there was hope of a better performance after half-time, it never materialised.
Within six minutes of the restart Watford missed two golden chances, with Doucoure first shooting into the side-netting from a tight angle four yards out, before a looping ball into the box found Sarr who scuffed an effort wide from a similar distance.
At the other end, Spurs nearly caught Watford napping as Dele Alli headed Aurier's cross over the bar, and the hosts were again exposed on the break as Son outpaced both centre-backs before firing just over from a good position.
Both sides were lacking a clinical finish and, after Vertonghen was penalised for handball on Deulofeu's shot, Deeney's penalty summed up the afternoon when his poor spot-kick was kept out by Gazzaniga.
That miss appeared to extinguish the spark in what had been a high-tempo encounter up to that point, until, in injury-time, Lamela slid in to turn Aurier's low ball towards goal, only for Pussetto - who had only been on the pitch for three minutes - to clear off the line and deny Jose Mourinho's side a much-needed win by a matter of inches.
What the managers said...
Watford head coach Nigel Pearson: "I've said many times that we might have to deal with a few difficult times, and sometimes that'll be losing or a disappointment that we should have won, but I've seen our players put in an incredibly honest performance and a very good one too."
Tottenham boss Jose Mourinho: "We started well, we played well and we finished well. It's not easy to come here and play with a team that is not physical but is just technical. Apart from the defenders we played with Winks, Lo Celso, Dele, Lamela, Lucas, Son.
"I think we have to adapt to what we have and we did it very well. It's not always the players, sometimes it's the way the team is used to compete. With Kane and Sissoko you'd find two physical players straight away."
Man of the match - Ismaila Sarr
On another day, on most other days, Sarr would have found himself with at least one assist after making four key passes and seemingly finding a man with every cross he put into the Tottenham box.
After a quiet opening half-hour he gave young Japhet Tanganga the runaround down the Watford right. It was his cross which Doucoure should have turned home just after the break, while he should have found the back of the net himself moments later.
He could say he made much of his own success - he won the ball back more times (10) than anyone on the Watford side, and Pearson will be praying the injury which forced him off late on is nothing serious.
Opta facts - Spurs misfire again
- Tottenham have failed to score in three consecutive Premier League games for the first time since November 2013. It's also just the second time a side managed by Jose Mourinho has failed to score in three league games in a row (Man Utd, October 2016).
- This result ended a run of 93 Premier League games without a 0-0 draw for Tottenham, the second longest such run in the competition's history (Man Utd, 114 games ending May 2002).
- No side has kept more Premier League clean sheets than Watford so far in 2019-20 (8). However, the Hornets have also failed to score in a league-high 11 Premier League games this season.
- There were 32 shots without a goal in this match, the most in a Premier League game without there being a goal since Crystal Palace v Cardiff in December 2018 (40).
Watford travel to relegation rivals Aston Villa on Tuesday night at 7.30pm, while Spurs host Norwich at the same time on Wednesday.