Fifty-three minutes in, and the Arsenal support were shouting the “Olés”, as their team hogged the ball and strayed perilously close to show-boating territory. It certainly made a change from “Wenger out” and veins bulging in foreheads, which has been the vibe at this stadium in recent matches.

Arsenal have not been this comfortable at home for some time, probably not since the 2-0 win against Bournemouth on 28 December and Arsène Wenger, the relentlessly under-fire manager, could take reassurance from a stroll.

It was impossible to believe that this was the same Watford who had won here in the FA Cup quarter-final three weeks previously. They barely contributed this time and it was left to Alex Iwobi, Arsenal’s 19-year-old attacking midfielder, to steal the show.

It felt fitting that as Arsenal remembered David Rocastle, who died 15 years ago this week, another academy product should step forward to impress. Iwobi created the opening goal for Alexis Sánchez while he scored the second himself and his performance was marked by fearlessness, mobility and cutting edge.

Wenger made the point that Iwobi, who came to Arsenal at the age of eight, was steeped in the club’s values – one of which was to give young players a chance. “Not many clubs can say that,” Wenger said, during a slightly haughty press conference.

He suggested that the principal difference between this performance from his team and some of those of late was their ruthlessness, which rather skated over other issues. “We had the same dominance in the cup tie against Watford but we could not score,” he said. “Recently, we haven’t made the maximum of our chances.”

Wenger also referenced the number of matches in different competitions that his team have had to play during what has been a disastrous run and it was easy to detect a measure of frustration in him. If only, Wenger might have said, Arsenal could have played a bit more like this from mid-January.

Watford have offered the impression that they are preoccupied with the FA Cup – they play their semi-final against Crystal Palace on 24 April – and it is remarkable that since the memorable home win over Liverpool on 20 December, they have won just two Premier League matches.

Quique Sánchez Flores’s team were second best and the die felt cast when they went behind early on. Iwobi picked out Sánchez with a ball in from the left and, having drifted in behind Nathan Aké, the Chilean extended Heurelho Gomes with a header before beating him on the rebound. Happily for Arsenal, Sánchez was in the mood.

Arsenal’s control of the first-half was total and so the thought occurred that they would allow Watford back to 1-1. Not here. They got the second goal when Francis Coquelin released Sánchez with an incisive pass and he returned Iwobi’s earlier assist with a smart cut-back. Iwobi arrived to slam a low, first-time shot past Gomes.

The Emirates crowd saluted the late, great Rocastle with applause in the seventh minute and there were other uplifting snap-shots, not least Héctor Bellerín’s Zidane-style 360 spin, which got him away from two Watford players. The Arsenal fans loved it when Mesut Özil jogged over to take a corner in front of the away enclosure, who booed him, as they were unhappy at what they perceived to have been a dive from him moments earlier. Özil responded by applauding them.

Arsenal might have been further in front by half-time. Danny Welbeck scuffed one chance and was narrowly off-target with another, while Iwobi worked Gomes with a wonderful curling effort and Sánchez did likewise with a free-kick.

Quique Sánchez Flores gestured at his substitute’s bench as soon as Sánchez had burst up the right to lay on the second and he hooked Étienne Capoue. The Frenchman, who had played at left midfield, jogged straight off down the tunnel; it is never anything but a humiliation to be withdrawn in the first half. Flores, who took off Odion Ighalo at half-time because he said the striker was tired after international duty with Nigeria, accepted responsibility for getting things wrong.

Bellerín scored the third straight after the interval with a shot that deflected off Ben Watson and, thereafter, Arsenal pressed cruise control. Iwobi hit the crossbar in the 50th minute and perhaps the stand-out memory of the second half was that of Allan Nyom scything through Özil, having been rattled by the Arsenal playmaker’s flicks and tricks. Nyom, who was booked, thought that Özil was taking the mickey.

For Watford, Sebastian Prödl had a header cleared off the line by Nacho Monreal and Troy Deeney was denied by an acrobatic save from David Ospina, but Arsenal had the last word when one substitute, Joel Campbell, beat Nyom and crossed for another, Theo Walcott, to tap home.