However, prior to the goal, Watford had put the ball out of play due to an injury and the hosts chose not to return possession from the resulting throw-in.
Gunners captain Pierre-Emerick Aubameyang had a first-half penalty saved by Ben Foster following a poor challenge by Danny Rose on Alexandre Lacazette – and the Watford goalkeeper produced another fine stop to keep out Gabriel’s header shortly before half-time.
The visitors were fired an early warning when Bukayo Saka had an eighth-minute finish ruled out for offside at Emirates Stadium.
Watford’s first attempt did not arrive until the 40th minute but Joshua King squandered the chance to earn a late point, shooting into the side-netting after pouncing on a mix-up between Aaron Ramsdale and Ben White.
Ranieri’s afternoon was made worse by Juraj Kucka’s late dismissal for a second yellow card late on and defeat leaves his side 17th, two points above the relegation places.
At the end of a week in which three Premier League bosses have lost their jobs, Arsenal appear to be reaping the rewards for standing by Arteta following a disappointing start to the campaign.
Leicester City were denied a winner as the video assistant referee ruled out a goal to force the Foxes to a 1-1 with Leeds United.
Leeds forward Raphinha had put his side deservedly in front in the 26th minute when his free-kick from out wide caught out Leicester keeper Kasper Schmeichel at his far post.
But Leicester responded seconds after the resulting kick-off with Barnes curling a stunner into the top corner from a tight angle.
Both sides had chances to win the game late on.
Ademola Lookman thought he had poked home the winner for Leicester City midway through the second period, but was standing in an offside position when Jamie Vardy had flicked on a Youri Tielemans corner.
Antonio Conte’s first Premier League game in charge of Tottenham ended in a hard-fought goalless draw against Everton at Goodison Park.
Conte has only had a few days to work with his players and kicked off his tenure with a 3-2 win over Vitesse in the Europa Conference League on Thursday, but this was a real gauge of the task at hand for the Italian.
Tottenham have gone more than three hours in the league without a shot on target but substitute Giovani lo Celso almost got Conte off to a winning start in the league when he curled an effort against the post with two minutes to go.
This was also a much improved Everton from recent weeks, although Rafael Benitez’s side, without a win in the top flight since September, had Mason Holgate dismissed late on for a high follow-through on Pierre-Emile Hojbjerg.
The hosts thought they had been handed a golden chance to break the deadlock when Chris Kavanagh awarded a penalty in the second half, only for the referee to overturn the decision after consulting the pitch-side monitor.
Richarlison appeared to beat Spurs goalkeeper Hugo Lloris to the ball and was brought down in the area but Kavanagh deemed that the Frenchman had got a fingertip to the ball.
Spurs enjoyed more possession and there were tentative signs of the traits imposed by Conte on his successful sides of the past, with the visitors showing more energy and intensity than previously this season.
But for all their possession it was Everton who looked more dangerous in a game of few chances, with Michael Keane heading over the bar and Demarai Gray turning an effort wide with 10 minutes to go.
It was perhaps a sign of Conte’s influence that one of Spurs’ best chances fell to wing-back Sergio Reguilon, who scooped over unmarked at the back post from Harry Kane’s cross before the break.
The draw keeps the teams a point apart, with Spurs ninth and Everton 11th – though both are within one win of the Europa League places.