If we take Jack Wilshere's word for it, the England midfielder smokes about as often as he scores. "Embarrassing" is how Wilshere described his goal ratio a few days before he was pictured outside a nightclub with a fag in his hand. A difficult week had a happy ending for Wilshere, however, as the 21-year-old scored only his second Premier League goal in Arsenal colours on a mixed afternoon in the Midlands.

In truth, for the best part of an hour it had looked like being another bad day at the office for Wilshere, who was restored to the starting lineup after being named among the substitutes against Napoli on Tuesday night. Deployed wide on the left, Wilshere was a picture of frustration during the opening 45 minutes.

He gave the ball away cheaply, struggled defensively, received a poke in the eye and, just to cap things off, was booked on the stroke of half-time for a lunge on Claudio Yacob, the Argentinian who had headed West Bromwich Albion in front moments earlier.

Indeed, when Tomas Rosicky removed his tracksuit top on the sidelines early in the second half, it would have been no surprise if the No10 had been displayed on the substitutes' board. Aaron Ramsey, though, was the player to make way and while that decision was met with surprise by the travelling supporters, and just about everyone else inside The Hawthorns, Arsène Wenger was vindicated four minutes later when Wilshere thrashed a 20-yard left-foot shot that deflected off Jonas Olsson's shins to beat Boaz Myhill.

It was only Wilshere's sixth Arsenal goal in 107 appearances in all competitions, and the first time he has scored in the league for the north London club since he got the fourth in a 4-2 win at Villa Park in November 2010. From that point on Wilshere looked like a completely different footballer. Confidence coursed through him as he went from being on the fringes of the game to one of Arsenal's most dangerous players.

A fine pass in the 76th minute provided evidence of his growing influence. Cutting in from the right, where he often popped up and generally looked much more at ease because of the opportunity to come inside on his left foot, Wilshere played an inch-perfect 30-yard pass that picked out the run of Olivier Giroud inside Gareth McAuley. Giroud, however, tried to take the ball around Myhill, who forced the striker wide and repelled the Frenchman's shot from a tight angle.

By that stage, Wilshere looked like he was enjoying himself, which should at least give the England manager, Roy Hodgson, some encouragement before the World Cup qualifiers against Montenegro and Poland across the next nine days.

"[Jack] had a difficult first half, where he was fouled a lot, but he showed he has character and kept going. And in the end it's good that he was rewarded," Wenger said. "I think also in the second half he gave some great balls to create chances."

For Wilshere, there will be relief that he is making the headlines for the right reasons after all the criticism that came his way as a result of being photographed with a cigarette. "He's an honest guy and when he's wrong, he knows it," Wenger said. "I think today the players don't get away with anything – they know that's the rules of modern society, they have to deal with it. I think he learns very quickly and what is more important for England and Arsenal is that he shows the right response on the pitch."

It is still hard to escape the feeling that Wilshere is not at home playing wide, even if Wenger believes that using him on the flanks will help him to get the burst of speed back into his game after all his injury problems over the past couple of years. At times, in the first half in particular, Wilshere seemed to be roaming across the pitch in desperate search of the ball more than anything else – something which tends to be less of a problem when he is playing in the centre of the field.

As for the goal, Wenger was delighted, but the Arsenal manager is not expecting it to become a habit. "I don't think he will ever be a goalscorer," Wenger said, "but he's a player who can provide chances for others. In our job, it's quite simple, you need players who score and players who give the balls to those who score. He's more in the second category but of course from that category you want a few goals as well, so it's good that he knows he can do it. Let's not forget we had the same problem with Ramsey a while ago. Once they start to score it comes naturally."