The Hornets captain had the chance to send his team ahead in the 70th minute of the contest but saw his effort saved by Paulo Gazzaniga as the points were shared in the early kickoff.
The result has seen Watford - now unbeaten in their last five league matches - move above West Ham United into 16th position in the Premier League table, while Spurs climb into seventh, eight points off fourth-placed Chelsea.
Tottenham had a shout for a penalty inside the first minute following a scramble inside the Watford box, but neither the referee nor VAR were interested. On the break, the hosts had a half-chance through Gerard Deulofeu, although the attacker's effort was always moving wide of the post.
An open start also saw Son Heung-min find space inside the Watford box in the third minute, but the South Korea international was closed out before he could release a shot.
Spurs, backed by a vocal away support, were the side making the early running at Vicarage Road, with Giovani Lo Celso in particular impressing in a slightly withdrawn position.
The Hornets had a chance of their own in the 17th minute when Ismaila Sarr found space inside the Spurs box, but the attacker curled his effort over the crossbar under pressure.
Nigel Pearson's side had another opportunity to cause the visitors a problem three minutes later when Japhet Tanganga felled Sarr, although Nathaniel Chalobah's free kick from a dangerous position was disappointing.
There was a stoppage in play around the 30-minute mark with referee Michael Olivier needing a replacement receiver from the fourth official, which just interrupted a flow of Tottenham pressure.
Foster had to keep out a curling effort from Lamela as the away team carved out a half-chance, before Deeney and Deulofeu threatened for Watford moments later down the other end of the field.
Gazzaniga then had to palm clear a dangerous cross from Chalobah as Pearson's side forced the issue with the first half approaching its final 10 minutes.
Lucas had a brilliant chance to send Tottenham ahead in the 38th minute when he broke into a one-on-one with Foster, but the experienced goalkeeper was on hand to make a brilliant save.
Son then volleyed over the crossbar from distance before Deeney headed into the arms of Gazzaniga down the other end as the two teams headed down the tunnel at 0-0 following an open first 45 minutes of action.
Watford had a huge chance to take the lead early in the second period when Abdoulaye Doucoure broke into Tottenham box after smart work from Sarr, but the midfielder could not turn home from close range.
Sarr had a chance of his own moments later after Deeney won a header inside the penalty area, but the 21-year-old missed the post as Spurs survived another dangerous moment.
Mourinho's team had a clear opportunity in the 53rd minute when Son picked out the head of Alli from a cross, only for the England international to send the ball over the crossbar.
Chances were arriving at both ends and Deeney had one deflected wide of the post in the 55th minute with both defences coming under pressure at the start of the second period.
There was a full-blown scuffle just before the hour as Doucoure clashed with Jan Vertonghen; VAR had a look at a possible red card for the Watford midfielder, but the incident ended with yellow cards being produced for both players.
Son broke clear moments later as Spurs had the chance to take the lead, but the South Korean fired over the crossbar with the score level entering the final 30 minutes.
VAR had a look at a possible penalty in the 64th minute following a deflected strike from Lamela which led to more anger inside the stadium, but play was allowed to continue.
Referee Oliver pointed to the spot in the 69th minute, though, with the ball striking the arm of Vertonghen inside the box. VAR agreed with the match official's decision, but Deeney saw his penalty saved by Gazzaniga.
The pressure on Spurs was relentless, though, and Mourinho responded by introducing Inter Milan-linked attacker Christian Eriksen in place of Alli, who had struggled to make his mark at Vicarage Road.
Sarr struck wide of the away side's goal in the 78th minute before Pearson made his first change of the match, introducing Roberto Pereyra for Chalobah. Meanwhile, Fernandes was introduced for his Tottenham debut in place of Lo Celso.
Lamela fired wide of the Watford post five minutes from time as both sides looked for a winner. Tottenham thought that they had scored in stoppage time when a scramble inside the home team's box led to the ball moving towards goal off the foot of Lamela, but debutant Ignacio Pussetto managed to clear before it crossed the line.
Next up for Watford is a trip to Aston Villa on Tuesday night, while Tottenham face a home game against basement side Norwich City one day later.
WATFORD (4-2-3-1): Foster; Mariappa, Dawson, Cathcart, Masina; Capoue, Chalobah (Pereyra 79'); Sarr (Pussetto 89'), Doukoure, Deulofeu; Deeney
TOTTENHAM HOTSPUR (4-3-3): Gazzaniga; Aurier, Alderweireld, Vertonghen, Tanganga; Winks, Lo Celso (Fernandes 79'), Alli (Eriksen 72'); Lamela, Lucas, Sonbody check tags ::