Paul Lambert's side produced a determined display at the Emirates Stadium on Saturday, recovering from going behind to an early Olivier Giroud strike as two goals from Christian Benteke, both after penalty awards, and a late breakaway from summer signing Anthony Luna secured a memorable victory.
For much of last season, Lambert's young side battled for survival, with their heavy defeat at Stamford Bridge on December 23 one of many forgettable outings.
Dutch defender Vlaar, though, believes it will be a very different game this time around in the hastily rearranged fixture because of Chelsea's involvement at the UEFA Super Cup.
He said: "If you can win at the Emirates, of course it is a great start. We want to do it again on Wednesday now. We all know (remember) what happened last year, so we want to put that to rest.
"We learnt a lot and we still have to learn a lot, but mentally we became a stronger team. We need everybody, all 25 players because it is a long season.
"The spirit is there in the group and that is the most important thing. To come back from an early goal was very good, and it was more than a win for us.
"You know when you play in eight days against Arsenal, Chelsea and Liverpool, that it could be a little easier, but it is the start of the season and nobody really knows a lot about each other, and what will happen from now."
Benteke may have been on the scoresheet, but Gabriel Agbonlahor impressed with his all-action attacking display and it was his penetrating runs which saw Arsenal concede both penalties.
Manager Lambert believes the 26-year-old, who last season became the club's leading Premier League goalscorer, can force his way into the England set-up again. His last cap was earned in 2009.