A goal in the 34th minute of the 45-minute match was all that separated the two sides, putting the north London team in with a good chance of victory in the friendly tournament
Arsene Wenger named an inexperienced team for the 45-minute game, with Marouane Chamakh and Kieran Gibbs the most recognisable first-team players and the left-back captaining the side. Right-back Carl Jenkinson also made an appearance, as well as Lansbury, who enjoyed a successful loan spell at West Ham last season.
Anderlecht began well, and had the ball in the net in the opening five minutes, but Tom de Sutter was adjudged to have been offside after Gunners keeper Damian Martinez made an error to let the striker in.
The Gunners' first chance of the game came after 23 minutes, when Chamakh lost his man to get onto Miquel's through ball, but saw his shot well saved by Anderlecht keeper Silvio Proto.
Arsenal youngster Thomas Eisfield was showing some nice touches, but looked a touch lightweight at times as both teams failed to create any real clear-cut chances.
Anderlecht were the next to come close, with Miquel blocking a shot on the line after Reynaldo twisted his way into the area.
But Arsenal found the break through after 34 minutes, with Carl Jenkinson putting in some nice work down the right-hand side before crossing for Lansbury to slam home at the front post.
Arsenal held on comfortably for the remaining 10 minutes, putting themselves in a good position to win the tournament with Southampton up next following their 1-0 defeat to the Belgian side.
Southampton went behind 15 minutes in as striker De Sutter tapped into an empty net after his initial shot had been blocked by Kelvin Davis. The hosts almost pulled level when Jos Hooiveld headed against the bar from Adam Lallana's corner just over five minutes later, but the Belgian team held on for the win against the newly promoted Premier League side.