The Welshman, Wojciech Szczesny, Tomas Rosicky and Mathieu Flamini all played in an otherwise youthful XI as the Gunners played for the first time since winning the FA Cup in May
In their first fixture since lifting the FA Cup in May, Arsene Wenger named a youthful starting XI before making wholesale changes at half-time.
Substitute Olsson opened the scoring with an impudent dink from inside the area eight minutes after the hour before Afobe doubled the lead from the spot late on.
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Yaya Sanogo spurned an early chance for the visitors when he shot straight at Boreham Wood goalkeeper James Russell.
Wenger's men continued to dominate possession with Ramsey next to go close with a low drive that flew marginally wide half an hour in.
Jon Toral should have scored shortly after following a well-worked move, but he sidefooted his shot wide.
The hosts enjoyed a late spell of pressure close to half-time, but both sides were goalless at the break.
Wenger made a host of changes at the break, with the likes of Kieran Gibbs, Tomas Rosicky, Flamini and Abou Diaby all getting a taste of the action.
Chuba Akpom, 18, was another introduction at the interval and he was quickly among the action, going close twice early in the second half.
Two substitutes then combined to end Arsenal's frustrations as Rosicky dinked a throughball into Olsson's path, with the Swedish midfielder chipping the ball over Russell.
The lively Akpom was fouled in the box four minutes from time, allowing Afobe to convert the second, with Arsenal now due to gear up for their next friendly against the New York Red Bulls in the United States.