The Clarets were reduced to 10-men when Jeff Hendrick received a straight red card for a two-footed challenge after just six minutes.
Troy Deeney broke the deadlock four minutes later before Niang headed José Holebas’ cross powerfully across goal and into the bottom corner.
Ashley Barnes scored from the penalty spot with 12 minutes remaining, but the Hornets managed to hold on to move into the top half of the table.
Deeney strikes after Hendrick red card
The visitors were reduced to 10-men after just six minutes when Hendrick lunged over the top of the ball and brought down Holebas.
It wasn’t long until the hosts made the extra man count, four minutes to be precise when captain Deeney headed past Tom Heaton.
The forward nodded Niang’s cross, which had the ‘keeper in two minds whether to come and collect the ball, into the bottom corner to break the deadlock.
Niang, who signed on loan from AC Milan, forced Heaton into making a fine save on 22 minutes before Deeney found Zarate, who volleyed fiercely at goal, which stung the gloves of the ‘keeper.
Niang nets first Premier League goal
Sean Dyche’s side, who haven't won an away game since last May, had their first chance of the game just after the half-hour mark, Joey Barton had Heurelho Gomes sprawling across to save his free-kick.
The hosts pushed on in search of a second goal, Niang was denied once more before Zarate curled just wide of the post three minutes before half-time.
However, the Hornets did break down their opponents once more before the break, and doubled their lead in the second minute of additional time.
Holebas crossed early and Niang headed across goal and into the bottom corner from around the penalty spot for his first goal since signing in the January transfer window.
Watford were content to sit on their lead, and the next opening in the game didn’t come until 70 minutes when Étienne Capoue tested Heaton from close range.
Barnes' penalty a consolation
The ‘keeper made the save of the match soon after when he made a brilliant reaction save after Deeney tried to head Niang’s cross back across goal.
However, the visitors continued to search for a route back into the game and their lifeline came when George Boyd’s shot struck the arm of Sebastian Prödl in the penalty area.
Barnes’ spot kick hit the inside of the post and nestled into the net, with Gomes rooted to the spot and the Clarets had 12 minutes to find an equaliser.
The goal spurred the visitors on and substitute Robbie Brady broke forward, but his dipping volley was saved by Gomes four minutes later.
Barnes capitalized on Craig Cathcart’s mistake on the edge of his own area, but his shot across goal was covered by the 'keeper.
Deeney thought he had his second goal of the game when he slotted home Isaac Success’ low cross, but it was ruled out for a handball in the build-up and the Hornets held on for a valuable three points.