Walcott - a controversial omission from the squad for the ill-fated FIFA World Cup™ campaign in South Africa - and under-21 international Wilshere are both expected to feature in the forthcoming European Championship qualifying campaign as Capello looks to rebuild a squad for the future.
It took Walcott, who looks fresh from a summer's rest, just three minutes to open up the Celtic defence as Carlos Vela swept the Gunners into the lead.
Wilshere, who was starting his second game of the weekend in central midfield, produced an all-action display which was almost capped by a goal but his stunning first-half volley smashed against the crossbar.
Arsenal manager Arsene Wenger will now look to continue his squad's fine pre-season form in their final friendly at Legia Warsaw next weekend, by which captain Cesc Fabregas will have returned from an extended holiday after winning the FIFA World Cup with Spain.
As expected, Wenger made some changes from the team which drew 1-1 with AC Milan on Saturday. Goalkeeper Manuel Almunia was handed a chance to stake his claim for Arsenal's number one jersey ahead of the Gunners' opening game of the Premier League season at Liverpool on 15 August.
Celtic, meanwhile, clearly had one eye on next week's crucial Champions League third qualifying round second leg against Braga, with the Portuguese side leading the tie 3-0.
Of today's XI, only goalkeeper Lukasz Zaluska and defender Jos Hooiveld appeared set to start at Parkhead on Wednesday night, while Aiden McGeady, heavily linked with a move away from the Scottish side, was not even on the bench.
It was a lively start by Arsenal, and no surprise when the hosts took an early lead. Wilshere played Walcott into the right side of the Celtic penalty area, and his shot across goal was turned in at the far post by Vela. Arsenal continued to press, with a 20-yard drive from Thomas Vermaelen forcing Zaluska into a good stop.
Celtic, who drew 2-2 with Lyon in their opening game, wasted a great chance when Daryl Murphy skewed the ball horribly wide from just inside the Arsenal box. On 34 minutes, Zaluska palmed away Walcott's free-kick, which was curling towards the top corner, before then flicking over a deflected shot from Wilshere.
From the resulting corner, Wilshere smashed an 18-yard, left-foot volley against the crossbar - and his headed rebound was plucked out of the air by the thankful Zaluska.
Arsenal doubled their advantage just before half-time when Celtic failed to clear a corner and full-back Bacary Sagna blasted an 18-yard angled drive inside the near post.
Substitute Samir Nasri swept the Gunners into a 3-0 lead on 51 minutes following more good work by Walcott down the right.
Wilshere then showed his inexperience by wrestling Celtic substitute Fortune to the floor in the penalty area on 69 minutes, but was let off when Greece international striker Georgios Samaras ballooned his spot-kick over the crossbar.
Almunia, who had not had much to do, pulled off a fine one-handed save to deny Efrain Juarez, but was beaten on 73 minutes when Murphy, a summer signing from Sunderland, knocked the ball in after it rebounded across the six-yard box.
The Arsenal goalkeeper denied Murphy when, with eight minutes left, the reshuffled home defence was opened up again, before Ki Sung-Yueng eventually made it 3-2 with a close-range effort.