Yaya Sanogo broke the deadlock in the second minute as he combined with Santi Cazorla before rolling his finish between Roman Weidenfeller’s legs.
The 21-year-old striker, who started ahead of Lukas Podolski, nearly added a second but Sanogo took too many touches and the chance was gone.
We played absolute solid at the back
However, Alexis Sanchez wrapped up three points with his 13th goal of the season, curling a powerful finish past the Dortmund goalkeeper.
“It was a solid performance, especially defensively,” Mertesacker told Sky Sports. “We didn’t give them too much, especially in the second half.
“We played absolute solid at the back. We had some disappointing results against opponents recently. It was a mental test. We can continue now.”
Asked if Arsenal needed to improve after recent results against Anderlecht, Swansea and Manchester United, Mertesacker added: “We had to [improve].
“After Anderlecht, Swansea and Manchester United, we dropped mentally a bit, but we came back even stronger. We learned form our disappointments.”
The Germany international urged Arsenal to produce another big performance at West Bromwich Albion on Saturday.
“We have to prove something in Saturday’s early kick-off. Last season, we dropped a lot of points. We can focus on the Premier League,” said Mertesacker.
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