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Arsene Wenger made 11 changes to the team that were beaten by Manchester United at the weekend, but the Frenchman's second string put in promising displays to give him a 700th win as Arsenal manager.
After injury-plagued Mathieu Debuchy started the rout in the 11th minute by drilling home his first goal for 1,082 days and Theo Walcott tapped in, two minutes before the break Wilshere ended his Arsenal goal drought that dated back to the final day of the 2014-15 Premier League season.
A Denis Polyakov own goal made it four early in the second period, before Olivier Giroud scored his sixth goal this term from the penalty spot and Mohamed Elneny completed the rout with 16 minutes left.
"It's a bit of a relief (that I scored). It's one of those games -- it didn't mean anything because we had topped the group," Wilshere told BT Sport.
"It's one of those games you need to be in the right mind -- we enjoyed it. We're happy to go into the next round. All we can do when we get our opportunity is give the manager a headache."
Arsenal finished four points clear of Red Star Belgrade at the top of Group H, as the Serbs joined them in the knockout stage with 1-0 win over struggling Bundesliga outfit Cologne.
Cologne, still waiting for a first Bundesliga win of the season, only needed a draw in Serbia to qualify after beating Arsenal last time out, but a Slavoljub Srnic goal sent their season from bad to worse.
French side Marseille sealed their spot in Monday's draw with a 0-0 draw against Salzburg to join the Austrians in progressing from Group I.
Rudi Garcia's Ligue 1 team moved into the last 32 for the second straight season.
Atalanta, coming off the back of a stunning 5-1 win at Everton a fortnight ago, edged out in-form Lyon 1-0 to finish top of Group E as Andrea Petagna scored his fourth goal of the season in the 10th minute.
Lyon could now be drawn to face one of the eight sides slipping down from the Champions League in the last 32, including Atletico Madrid and Napoli.
Everton bow out with win
Everton made it two wins from two under new manager Sam Allardyce by cruising to a 3-0 victory over Apollon Limassol in Cyprus, although the former England boss did not travel with the squad due to a medical appointment.
Forward Ademola Lookman, 20, scored a double with close-season signing Nikola Vlasic adding a late third to salvage some pride for Everton as they avoided finishing bottom of the group.
"It's been good (under Sam Allardyce). Different training, different tactics. I'm enjoying it," Lookman told BT Sport.
Former Chelsea defender Branislav Ivanovic's brilliant overhead kick helped Zenit St Petersburg beat Real Sociedad 3-1 to finish first ahead of the Spaniards in Group L.
Gennaro Gattuso is still waiting for a first win as AC Milan coach after a 2-0 loss at Rijeka following their embarrassing draw at Serie A minnows Benevento at the weekend.
But the Croatian outfit missed out on joining Milan in the last 32 as AEK Athens pipped them to second courtesy of a goalless draw at Austria Vienna.
Moldovan side Sheriff Tiraspol slipped from first to third in Group F after a 2-0 defeat by FC Copenhagen, dropping below the Danes and group winners Lokomotiv Moscow, who beat bottom side FC Zlin by the same score.
Two-time runners-up Athletic Bilbao also qualified with a 2-0 win at Ukrainians Zorya Luhansk.
