Lacazette put the home side in front just after the 10-minute mark, slotting home from the penalty spot after Nesta Guinness-Walker fouled Gabriel Martinelli in the area.
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The League One side dug in after conceding the early goal and managed to keep Arsenal at bay for the remainder of the first half, which ended 1-0 in favour of the Gunners.
Arsenal continued to struggle to find a second goal until 60th-minute substitute Emile Smith-Rowe turned home a chance from the centre of the area, with Lacazette turning provider to make it 2-0 for Mikel Arteta's side.