England Under-21 international goalkeeper Scott Loach let Adrian Mariappa's back-pass slip under his foot and into the net to give the Robins an equaliser within 24 seconds of the second half on Tuesday night.
The Hornets had taken the lead through left-back Carl Dickinson's swerving shot and doubled their advantage when Craig Beattie notched his first goal for the club.
But the Robins pulled a goal back just before half-time when Marvin Elliott crashed in a thumping header.
It was the least Derek McInnes' side deserved and they will claim they earned their slice of luck which they got through Mariappa's own goal.
The draw leaves the Robins in 20th in the Championship table, level on points with Nottingham Forest who occupy the last relegation spot.
Visiting goalkeeper David James was given a taste of things to come in the 14th minute when Mark Yeates' long-range free-kick zipped through the air before falling narrowly wide.
The opening goal came from a similar distance in the 25th minute and from an unlikely source in Dickinson.
Watford worked the ball across the middle of the park, with Michael Kightly rolling the ball to Dickinson. He took one touch before unleashing a swerving effort from 25 yards out which flew past James and into the top corner.
Despite the visitors dominating large parts of the first half, it was the hosts who scored again three minutes before half-time through loanee Craig Beattie.
Yeates tried his luck from distance and his deflected effort took a dramatic dip before cannoning back off the crossbar. James was rooted to the spot and striker Beattie reacted quickest, nodding the ball into the net.
But McInnes' side were rewarded when Elliott's goal reduced the arrears moments before the interval.
An inviting cross from the marauding Ryan McGivern provided Elliott with a chance to drift in from the wing and leap higher than Dickinson to head home.
The visitors were gifted an equaliser in bizarre circumstances after a huge mishap from the otherwise impressive Loach.
The goalkeeper was under no pressure when he received the ball back from Mariappa but he took his eye off the ball and it rolled under his foot and into the net.
Neither side seemed content with a point and there were plenty of chances for a second-half winner.
Albert Adomah drove a shot wide while James turned Chris Iwelumo's shot around a post at the other end.
Kightly was involved in virtually every attack for the home side and he smashed the ball into the side netting before miskicking another chance when well placed.
But it was Watford substitute Troy Deeney who came closest to netting a winner with the last kick of the game. Iwelumo laid it back for the striker and his effort went just wide with James beaten.