The Clarets should have taken the lead as early as the second minute when Chris McCann fed Kyle Lafferty, but the Northern Ireland International placed his shot wide of the far post.
The home side had an even better chance after only ten minutes when Leigh Bromby's back-pass sold goalkeeper Richard Lee short and his attempted clearance was charged down by McCann to striker Ade Akinbiyi.
However, he pulled his shot wide of an empty goal much to the astonishment of all who saw it.
The striker had a chance to atone for his terrible miss, but glanced a header wide of the far post following a Wade Elliott corner.
These misses were to prove expensive as the Hornets took the lead from a Jobi McAnuff corner which was glanced home by the head of striker Darius Henderson.
The visitors had a chance to extend their lead shortly afterwards, but goalkeeper Brian Jensen saved firstly from Nathan Ellington and then diverted the rebound from Henderson round the post for a corner.
The second half commenced in a similar manner to the first with Elliott seeing his shot spilt by goalkeeper Lee and Akinbiyi forcing a header into the net only to be ruled offside.
Akinbiyi then wasted another glorious opportunity heading over the cross bar from close range after Lee had parried a shot from Lafferty.
Burnley came even closer when from a corner by sub Blake, Chris McCann headed against the post, whilst at the other end McAnuff had the opportunity to win the game but blazed his shot wide.
That was to prove an expensive miss as moments later Burnley were on level terms with Andrew Cole back-heeling the ball into the path of Blake, who made no mistake with a powerful right-foot finish.
Watford went ahead for the second time on 85 minutes as Burnley failed to clear a free-kick and sub Jordan Stewart lashed home a fine left-foot volley.
But that was not the end of the drama as Owen Coyle's side showed tremendous resilience to equalise for a second time with only a couple of minutes remaining.
Once again it was a cool finish from Blake after Graham Alexander had picked out opposite full-back John Harley and his volleyed cross that found its way through to Blake, who finished in fine style to earn his team a share of the points.