Mesut Ozil also scored twice, while Aaron Ramsey added another to fire the Gunners to a 4-1 victory, which was put into motion by a brilliant 18th-minute team move in which Wilshere was heavily involved.
The England international midfielder started the build-up in his own half, before collecting a pass from Santi Cazorla, exchanging flicks with Olivier Giroud and steering the Frenchman's clever return into the bottom corner with a delicate first-time finish.
"All the goals were great, but the first was exceptional and improvised," Wenger told reporters. "It was certainly one of the best [Arsenal] goals, one I enjoyed the most because it was a team goal."
"It had combinations and speed which you would always like your team to play with. This one was a mixture of technical quality, speedy thinking, quick reaction and as well being calm in front of goal.
"It had nearly everything you want to have, it was a great goal."
You can view Wilshere's strike, his second in as many Arsenal games, via the video below.