Arsenal extended their unbeaten start to 2017 as they coasted into the FA Cup fifth round by comfortably disposing of Southampton, with Theo Walcott marking his return from a calf injury by bagging a hat-trick against his former club and Danny Welbeck scoring twice.

Arsenal put in a near-perfect away performance, with Arsène Wenger watching from the stands following his touchline ban. It was a display that ought to stand them in good stead too, with their next three away matches at Chelsea, Bayern Munich and Liverpool.

Wenger was serving the first game of his four-match ban and communicated through an earpiece to his assistant, Steve Bould, and first-team coaches but stood to applaud Welbeck’s opener. It was his first Arsenal goal since last April and his first double since England beat Slovenia at Wembley in 2014.

It has been a long road back for Welbeck, who was making his first start for the club since he sustained knee cartilage damage on the penultimate day of last season at Manchester City, and Wenger admitted he wondered whether the striker would return to his best after his injury troubles. “You wonder, I wondered first of all whether he would be solid enough mentally and secondly you hope that will all go well after the second surgery,” he said.

“You have always two fears, the first that it takes too long to get decision-making and secondly that the player is scared to go into contact so when he made the runs and was fighting with defenders, that was a very important moment for him.

“He worked very hard, he went through some moments of very deep disappointment because he had a setback and then he had to go in again [for more surgery] on the knee. After the first disappointment he became even more resilient and worked even harder. He’s highly respected at the club because he’s shown so much dedication and has never moaned.”

It was a harsh lesson for Claude Puel’s young Saints and character building if nothing else, in the first FA Cup meeting between the sides since Robert Pirès’s winner in the 2003 final.

Both teams were unrecognisable from their last matches – with both managers making 10 changes – but Arsenal played with their trademark attacking verve and curiosity. Only Shkodran Mustafi survived from the team who defeated Burnley last Sunday, with the former Southampton pair Walcott and Alex Oxlade-Chamberlain named in Wenger’s very attack-minded starting lineup.

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Neither Aaron Ramsey nor Francis Coquelin travelled to St Mary’s, but Oxlade-Chamberlain and Ainsley Maitland-Niles impressed as unorthodox central midfielders. There was room, though, for Alexis Sánchez to squeeze on to the substitutes’ bench.

This was Southampton’s eighth match this month and Puel’s side were second best throughout. Shane Long was captain of a lineup with only 38 starts in the Premier League between them.

Arsenal were immediately on top, with Jeff Reine-Adélaïde having a shot deflected wide after three minutes. The 19-year-old had his chance after Walcott put on the afterburners in front of the Kingsland Stand, just as he used to as a teenager before joining Arsenal from Southampton in 2006.

It was only a matter of time before Arsenal opened the scoring, with Saints camped out inside their own half for much of this tie. Welbeck, making his first start for 265 days, obliged after 15 minutes, after Lucas Pérez sought him out with a neat no-look through ball and Welbeck dinked the ball over the teenage goalkeeper Harry Lewis and in off the crossbar.

Wenger stood up to clap Welbeck’s opener from the director’s box and the Arsenal manager was back on his feet seven minutes later. Welbeck doubled his and Arsenal’s tally after converting Oxlade-Chamberlain’s magnificent lofted ball that cut out the entire Southampton backline. Welbeck controlled the ball with a majestic first touch before poking beyond Lewis with his second. Welbeck wheeled off towards the corner flag to celebrate while the defender Jack Stephens could only crash into the post as he attempted to hook the ball clear. Arsenal were in cruise control.

Long had a half a chance for Saints, forcing David Ospina into a stop from a tight angle after a clever through ball by Cuco Martina but Arsenal were unrelenting.

Walcott then tapped home Welbeck’s low cross from the left, as Southampton’s hopes of dumping Arsenal out of both domestic cups vanished before their eyes inside 35 minutes.

Despite their comfortable lead, Wenger introduced Sánchez shortly after the hour, as Welbeck left the field to a standing ovation.

Sánchez had been on the field for only four minutes but made an impact, laying the ball on a plate for Walcott to add his second goal of the match and deliver Arsenal a fourth. Walcott then completed the rout, sealing his hat-trick after Sánchez rolled a low ball across the box for the forward, who put the gloss on a sublime team performance.

“It’s a disappointment for our fans and for our young players it was a good lesson,” Puel said. “It’s very hard now but the players will learn a lot for the future.”