The Gunners' 2-1 win at Swansea on Saturday extended a club-record run of consecutive away victories to 12 and put them two points clear at the top of the Barclays Premier League table.
Too often in recent seasons Arsene Wenger's side have paid the price for their fallibility on the road, but Wilshere believes the current sequence, allied to making the most of defeats for Manchester United and Manchester City over the weekend, show there is a new edge about Arsenal this season.
"We started that towards the end of last season. We knew we had to win games because we had to get that fourth spot," said the England international.
"We were going towards the end of the season, knowing that because we had dropped points earlier in the season, we had to win games.
"I think we have continued that into this season and that's vital in this league. You saw that Manchester United and Manchester City slipped up and I remember a few years ago when I broke into the team, when they lost, we lost. We failed to capitalise, but this time we did, which is nice.
"I think we showed a different side to our game and hopefully we can continue that."
Aaron Ramsey was once again the inspiration for Arsenal at the Liberty Stadium, creating Serge Gnabry's opener and scoring the second himself.
Ramsey has made an outstanding start to the season, and is showing the sort of form many had known he was capable of before he suffered the setback of breaking his leg at Stoke in 2010.
The Welshman has scored eight goals in eight games to help the Gunners recover from their opening-day defeat against Aston Villa to top the Premier League and their Champions League group.
Arsene Wenger is not short of talent in midfield with Wilshere, Mesut Ozil and Mikel Arteta, while Santi Cazorla is currently sidelined through injury.
But it is Ramsey who has been the driving force behind their revival, and Wilshere was full of praise for the 22-year-old.
"His fitness levels are not normal," said Wilshere.
"He's naturally so fit he can score at any time in the game. You can see that. He's pushing on in the 94th minute. Not many players can do that.
"He's got his confidence back, which is nice to see.
"If he carries on playing the way he is and working hard, he can improve further.
"He's got a great appetite for the game. He wants to improve. He's training all the time. He's not missing a training session, he's fit, he's young and he's showing his best form.
"Hopefully he can continue it and get even better."