The circumstances might have been low-key compared to Wenger-Ferguson duels of old, but the second generation of a legendary footballing family did his upmost to ensure it was an edgy, vehemently competed affair as Arsenal squeaked past Doncaster Rovers. Darren Ferguson’s team gave Arsenal a fright as a contest that looked relatively comfortable in the first half turned into a nail-biter.

The Carabao Cup might not be a priority – the lowest recorded crowd since Arsenal moved to the Emirates of 44,064 attested to a certain lack of enthusiasm in north London – but Doncaster and their merry followers were able to admire a battling performance that belied their position in the lower reaches of League One.

Arsenal did enough thanks to Theo Walcott’s neatly taken dink of a match-winning goal. But the real boon belonged to the man who walked off the pitch with his shirt off and a big thumbs-up for the crowd. Jack Wilshere completed 90 minutes for Arsenal for the first time in almost three years. That is a meaningful statistic for a player who has had more than his fair share of setbacks.

Wilshere’s creative performance shone a light on the qualities he is capable of bringing to his team from the heart of midfield. Against opponents where there was space to look and think, he relished the opportunity to orchestrate, to spray passes with elan and to direct traffic with quick thinking and clear vision. He was not in a situation where he had to overstretch and over-compete, which suited him well. It was a positive stride along the road to recovery at his boyhood club that has had plenty of potholes.

Arsène Wenger felt the opportunity was perfect for Wilshere. “I wanted to leave him on to give him 90 minutes. Overall it was the ideal game for him to gain confidence and fitness,” he said. “We will see how he responds now. He is available now to play – the decision is when to play him. He needs 90 minutes of intensity repeated. He will soon be back. Everyone is looking at him. Everyone expects him to come back to his best. I wish that as well.”

Even though Wenger tends to favour what he calls a “mixed” line-up in these less significant challenges on the season’s wish-list, it was a surprise to see Alexis Sánchez in the starting XI. Any kind of injury picked up in a game like this would have opened up a supersized can of worms. But from Wenger’s perspective the Chilean, who had an extended summer holiday, still needed minutes in his legs to regain full sharpness. This was another useful 90-minute workout.

Some players who warrant the Champions League platform might coast through a Carabao Cup run-out but not Sánchez. His motivation was fully charged. His hunger to play manifested itself in a display full of chasing causes, darting runs and a willingness to shoot.

It was his instinct for a raking attacking pass that provided Arsenal with the decisive goal, which invited Walcott to finish past the goalkeeper Ian Lawlor. The home team had the chances to open up a comfortable lead and Olivier Giroud will wonder how he did not manage to claim his 100th Arsenal goal after a series of decent efforts, while Walcott ought to have added more.

Doncaster were satisfied to go in at half-time still in contention, with enough encouraging moments of their own to give them hope. As the game wore on Arsenal became more ragged and Doncaster’s determined attitude as they chased an equaliser won the hearts of the massed visiting support in the Clock end.

By the end Arsenal’s strangely imbalanced defensive line-up was on the rocks and Rovers went agonisingly close. Ben Whiteman had a free run at goal. Liam Mandeville’s clever cut-back and shot was deflected. Matty Blair’s header hit the crossbar. Despite their valiant efforts, it was not to be.

“I am proud of the players,” Ferguson said. “They did a lot of the things asked. It was a fantastic learning curve in terms of concentration levels.” Arsenal ticked this off and will host Norwich City in the next round.