Nouioui opened the scoring when he stroked into an empty net in the 73rd minute, having only come on for Kris Commons four minutes earlier. Charlie Mulgrew added a second against his former club three minutes later.
The only change to the Aberdeen side that beat St Johnstone last week saw Gavin Rae return in place of Clark Robertson, while Celtic made three alterations, with Tony Watt, Mikael Lustig and Beram Kayal replacing Miku, Scott Brown and Joe Ledley.
By and large, though, it was a scrappy opening period, with neither side taking command of the midfield, and possession being surrendered easily and cheaply by both sides.
The Hoops' first real chance came on the quarter-hour when former Don Mulgrew's corner was headed over by Victor Wanyama.
Both sides were now beginning to probe and when Rae won the ball in midfield he fed the precocious Fraser, who tested Fraser Forster with a right-footed effort from 20 yards.
Celtic came closest yet as Kris Commons retrieved a half-cleared Mulgrew corner on the left and swung a dangerous cross to the far post, where Watt headed off the base of the post.
Just after the half-hour, Chris Clark created space to cross from the left for the Dons and though Niall McGinn got in the way of an initial header from Magennis, the former Celtic man reacted quickly to send a low shot narrowly wide of Forster's right-hand upright.
Aberdeen, who enjoyed some early pressure in the second period, were dealt a blow when Ryan Fraser was again forced off just after the hour, limping from the pitch to be replaced by Scott Vernon.
The Dons were undeterred, however, and after 68 minutes they had their best chance yet. McGinn cut the ball back for Hayes, and the Irishman set himself before firing low into the side netting.
But the deadlock was finally broken five minutes later, and the goal came for Celtic. Wanyama crashed a 25-yard shot off Jamie Langfield's left-hand post, and all newcomer Nouioui had to do was roll the ball home.
Boosted by their goal, Celtic added a second just three minutes later. Samaras crossed from the left and, at the back post, Mulgrew acrobatically volleyed home left-footed.
The visitors had the ball in the net again when Wanyama headed home at the back post, but the flag had already been raised for offside against the Celtic man.