The Hornets were no match for Pompey in Monday's Championship clash at Fratton Park.
Futacs scored in his second successive match with a header from David Norris' cross to give the hosts a deserved lead nine minutes after the interval.
Watford goalkeeper Scott Loach was shown a straight red card for hauling down Futacs outside the box, and then Mullins made sure of the victory after converting from Erik Huseklepp's cross.
The win ensured Portsmouth claimed their first victory in four matches and leapt above Watford in the table.
Portsmouth were forced to make two changes from the side that drew 1-1 with Leicester on New Year's Eve, with suspended duo Joel Ward and Greg Halford replaced by Tal Ben-Haim and Huseklepp.
Unchanged Watford started well and striker Troy Deeney was only inches away from getting a touch on Mark Yeates' cross.
At the other end, Huseklepp was trying to make the most of his opportunity and he struck wide from just outside the area on two occasions.
David Norris also missed the target from 20 yards as Pompey started to gain the upper hand, while Watford goalkeeper Loach did magnificently to claw Dave Kitson's effort from the edge of the box round the post.
Kitson was at the fore once again and the striker should have done better with his shot that cleared the bar after being given time and space to pick his spot.
The Hornets were by no means being outclassed but they were failing to fashion any meaningful chances until Marvin Sordell's shot deflected narrowly wide on the stroke of half-time.
It would have been harsh on Portsmouth, who regained the ascendancy in the early stages of the second-half.
Kitson headed weakly at Roach from Joe Mattock's centre and although the Watford shot-stopper superbly turned away a long range effort from Liam Lawrence, the hosts took a 54th-minute lead from the resulting corner.
Norris collected the ball from Lawrence's short corner on the right before he crossed for striker Futacs to head home on his first home start.
It was the Hungarian's second goal in as many games and was just reward for a fine all-round display.
Not content to hold on to a lead, Portsmouth continued to attack the Watford goal with gusto and a free-flowing move ended with David Norris forcing Loach into making another fine save.
Lawrence thought he had sealed the points when he tapped in after Mattock's long range shot had been deflected into his path, but there was a late offside flag.
Watford's afternoon went from bad to worse when Futacs burst clear and was impeded by Loach, who was sent off.
Mullins wrapped up the points for Pompey in the 87th minute when he collected the ball from Huseklepp's cross and lashed past substitute keeper Jonathan Bond at the second attempt