Liverpool started slowly but took the lead at the break after Mohamed Salah finished off a counter-attack with a lovely curling finish.
The Hornets should arguably be ahead but Abdoulaye Doucoure and Ismaila Sarr both missed two excellent chances while completely unmarked in the box.
Second half kicked off with the Reds still in full control, 50th minute – Mane flicks an outstanding header beyond Foster after an excellent cross from Shaqiri on the left following the corner to make it 2-0.
But VAR check rules that Mane’s arm was marginally offside and the goal was disallowed.
90th minute, the Egyptian nets his second after Mane’s cutback was mis-hit by Origi, allowing Salah to backheel in at the near post to secure all 3 points for Jurgen Klopp’s men.
Liverpool have an EFL Cup quarter-final against Aston Villa next, with the Club World Cup soon to follow.
Meanwhile, Watford will host Manchester United in the Premier League next weekend.