The north London side edged into a first-half lead courtesy of Erik Lamela’s brilliant individual goal before Nathan Ake was sent off for a dangerous challenge.
However, the Hornets could have taken the lead but were denied a winner by goal-line technology before substitute Son Heung-min netted a back-heel in added time.
Spurs have won their last three Premier League games following a 2-1 defeat by Newcastle United at White Hart Lane earlier this month, boosting their title hopes.
Speaking to BBC Sport following Tottenham’s last-gasp win at Watford, Pochettino addressed growing talk of the north London side winning the Premier League this season.
“In football a lot can happen the most important thing is we believe, we have a strong squad to squad to fight for it,” Pochettino said.
Spurs are four points behind new Premier League leaders Arsenal following Monday afternoon’s win.
The Foxes host title rivals Manchester City at King Power Stadium on Tuesday night.
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