The home side went into the game without a victory in 10 matches and having lost five successive games at Vicarage Road.
But Sannino's side got off to the ideal start when Dan Shittu was sent off for bringing down Troy Deeney inside the first 10 minutes and the striker converted the resultant penalty.
Fernando Forestieri, Ikechi Anya and Lewis McGugan, from the Hornets' second penalty of the match, completed the win.
With Watford's head of medical Marco Cesarini acting as interpreter, Sannino said: "It was a win against 10 men. We have to be happy for our supporters and for the three points that we had today because it [a win] was missing for a long time.
"I'm very happy for my players, for the supporters, a thought goes to Gianfranco Zola as well and we wait for the next game which, for sure, will be a tougher game (against QPR).
"We had the chance to play 11 versus 10. Normally with this type of game, if you don't play with your head you can have trouble. My players were fantastic because they were waiting for the right moment to go deep and to score.
"I would like to enjoy this moment but also to forget very quickly this win because in three days we have to play."
Asked what he had tried to do differently to the previous five home games Watford had lost under Zola, Sannino replied: "I'm not a magician but I'm an honest worker. I try to give a working mentality always to my players. It's only through the work that we can improve and have results."
Millwall boss Steve Lomas said: "We came with a game plan. Obviously Watford hadn't won in quite a while so we wanted to come and quieten the crowd.
"The last thing we wanted is a start like that and to concede a penalty and to get a man sent off. It was absolutely catastrophic.
"Obviously we knew it was going to be a long day after that. Steve Morison's had a chance to make it 1-1 but once the second goes in you know it's going to be a long, long day."
The Millwall fans chanted for Lomas to lose his job at various stages of the game but he said: "I always knew the situation. The buck stops with me, I'm the manager, simple as that, but we've just got to get on with it.
"We've got another game in two days, we've got to regroup, see who's fit and try and put in a performance that shows the fans the players are fighting for them as much as me."