Celtic ran out 2-0 winner in this afternoon's pre-season friendly in Glasgow, as Maeda and Turnball netted in front of a lively home crowd.
The home side started the game very much on the front foot, putting pressure on City in the their own during lots of the first half.
Although the first ten minutes of the game were spent predominantly inside City's half, the Canaries defended well and kept the home side from taking any of their chances in the box.
Reo Hatate and Joao Neves Filipe Jota worked the right wing together to slot numerous crosses into Tim Krul's box, but neither could find an opportunity on the receiving end.
The City midfield were able to hold the most possession inside 20 minutes, with Todd Cantwell making key interceptions and showing strength on the ball.
Norwich's defence continued to hold strong, as Andrew Omobamidele was called into action to keep the Hoops at bay in the box with a towering header to clear.
The Yellows' first piece of action came from a Max Aarons run down the right wing who crossed to Danel Sinani on the edge of the box, but City were then forced back to Mccallum with a high press from Celtic.
Teemu Pukki also looked to get in on the action after 18 minutes, when a cross from Milot Rashica met the Finnish international, but loops onto the roof of the net.
At the 25 minute mark, Aarons had a shot at goal from the edge of the box after a spell of possession, which forced Joe Hart to punch the ball away from danger.
Grant Hanley made successive blocks inside the box from the right wing to deny Jota from putting Celtic ahead, as the Portuguese winger had looked lively all half.
Cantwell's positive play allowed him to find space to shoot after 35 minutes, when his strong volley looked to be going on target, before Cameron Carter-Vickers blocked the shot.
Only a minute later, Celtic were able to capitalise on their high pressing and Daizen Maeda put the home side ahead, flicking a ball out of Krul's reach, into the net.
The final ten minutes of the half left Norwich defending deep, trying to keep the deficit at just one.
City then looked in trouble when the skipper went down unprovoked and had to receive treatment, but Hanley was up again minutes later to finish the half.
Hanley was replaced by Jacob Sorensen as the two sides returned from the tunnel going into the final 45 minutes.
Celtic started the second half with the same intensity as the first, making City work to keep the ball out of the box.
Norwich seemed to find some rhythm ten minutes into the second half, as Pukki and Sargent were able to link up to allow Rashica to fire on target, only to be denied by Hart in between the sticks.
Josh Sargent was later able to collect a pass from Sinani and parry a cross into the box, only to be unable to find a Yellows shirt on the end of it.
Celtic then continued their press on the Yellows and found a breakthrough in the 67th minute, when substitute David Turnbull took aim at Angus Gunn and found the back of the net.
Following the goal, City had spells of possession that looked dangerous on the attack, including a run from Hernández on the left wing that allowed him to take a shot on target, but the ultimate shot was blocked and cleared from danger.
Gunn made one final crucial sale in injury time, as he tipped away a powerful strike to the right side of the post, keeping the score at 2-0.
Celtic: Hart, Juranovic (Bernabei 59), Welsh (Jenz 59), Carter-Vickers (Jullien 84), Taylor (Abada 59), McGregor (McCarthy 84), Hatate (Mooy 77), O'Riley (Turnbull 59), Jota (Giakoumakis 59), Maeda (Forrest 59), Kyogo (Abada 59)
Subs not used: Bain, Siegrist, Jenz, Ideguchi, Ralston
Goals: Maeda (36), Turnball (67)
Norwich City: Krul (Gunn 60), Aarons, Omobamidele, Hanley (Sørensen 46), McCallum (Giannoulis 80), McLean, Cantwell, Sinani, Rashica (Hernández 80), Sargent (Idah 80), Pukki (Hugill 72)
Subs not used: McGovern, Tomkinson, Hills, Shipley, Gibbs, Riley, Rowe, Kamara
HT: 1-0
Venue: Celtic Park