France international Digne beat Ben Foster from a set-piece in the 96th minute to save Silva from defeat against the team that sacked him last January following links to Everton.
Watford looked set to triumph when Abdoulaye Doucoure scored two minutes after an own goal from Seamus Coleman to overturn former Hornet Richarlison's first-half opener.
Richarlison required just 15 minutes to get off the mark in controversial circumstances, side-footing Andre Gomes' squared pass home despite Theo Walcott touching the ball from an offside position.
Watford grew into the first half and squandered another good opening seven minutes before the break when Roberto Pereyra glanced wide following some positive play from Ken Sema on the right.
The visitors equalised in the 63rd minute when Coleman inadvertently sent the ball into his own net after Pereyra's header came back off the upright, sparking an incredible series of events.
Doucoure seemingly completed the turnaround 130 seconds later with a powerful header into the ground and past Jordan Pickford, taking advantage of a deflection on Pereyra's cross.
No sooner had Watford's celebrations died down, Everton wasted a big opportunity to equalise - Sigurdsson seeing his penalty kept out down the middle by Foster following Christian Kabasele's clumsy challenge on Yerry Mina.
Just when Javi Gracia's side looked to have done enough to draw level on points with their opponents, Digne curled a delicate 20-yard strike home to punish Kabasele for a needless handball.
Both sides continue to stutter
Despite the late leveller, Everton's underwhelming run of form continued. They have drawn three, lost two and won two of their last seven top-flight matches to sit outside the Europa League places and in need of some momentum.
Momentum was not a word associated with Watford ahead of this match, and they were denied a first win since the end of October to remain outside the Premier League's top half. On the brink of just a third away triumph of the season, the late twist may make this result feel as bad as the successive losses to Liverpool, Leicester City and Manchester City.
Digne digs Everton out of trouble
The former Barcelona defender took matters into his own hands after seeing Sigurdsson eye up the late free-kick, sending it out of Foster's reach to rescue what seemed an unlikely point. Digne also created three chances for his team-mates as he proved a regular threat attacking down the left.
