Substitute Maciej Zurawski breached a stubborn Aberdeen defence to secure a hard-fought victory for Celtic.
The visitors thwarted Celtic with some superb saves from Jamie Langfield and Gary Dempsey, industrious in midfield.
Kenny Miller spurned a glorious chance in 43 minutes after Lee Naylor's shot was saved.
Celtic broke the deadlock in 71 minutes - to the relief of anxious home fans - when Zurawski swept home Naylor's cross from six yards.
Thomas Gravesen returned from a thigh injury to take his place in the Celtic midfield for the visit of Aberdeen.
The Dane took over from Jiri Jarosik, who moved up to partner Kenny Miller in attack, with Zurawski dropping to the bench.
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Shaun Maloney's ankle injury sustained against Hibernian last Sunday meant he missed out, the Hoops' midfielder replaced by Aiden McGeady.
Aberdeen kept the same side which beat Dunfermline 3-0 last week although former Celtic midfielder Jamie Smith recovered from a groin injury to take his place on the bench.
The home side looked threatening from set pieces in the opening 10 minutes with Stephen McManus and Jiri Jarosik coming close with headers from Nakamura corners.
Thomas Gravesen then forced a smart save from goalkeeper Jamie Langfield in 14 minutes with a shot from 20 yards.
Aberdeen were struggling to fashion many attacking forays into the Celtic half in the opening stages.
The Dons rarely threatened, but Darren Mackie forced a great save from Artur Boruc in the opening period.
The home fans were becoming frustrated as Celtic could not find a way to penetrate the Dons' defence.
Aiden McGeady's shot in 41 minutes was heading for the top left-hand corner until Jamie Langfield clawed it away for a corner.
Kenny Miller missed a golden opportunity just before half-time when he missed from four yards after Lee Naylor's initial strike was saved by Langfield.
In the second half, the visitors grew in stature with Gary Dempsey outstanding in the centre of midfield.
Nakamura was at the heart of most of Celtic's advances, but his crisp passing often did not get the end product it deserved.
McGeady was denied by Langfield with half an hour to go, and Foster cleared the danger.
Zurawski replaced Thomas Gravesen in 66 minutes as Gordon Strachan opted to play with two natural forwards.
Boruc denied Aberdeen captain Russell Anderson an equaliser with a wonderful save from his bulleted header in injury time.
Celtic: Boruc, Telfer, Balde, McManus, Naylor, Nakamura, Lennon, Gravesen (Zurawski 67), McGeady, Jarosik, Miller (Pearson 87). Subs Not Used: Marshall, Sno, Riordan, Wilson, O'Dea.
Booked: McGeady.
Goals: Zurawski 72.
Aberdeen: Langfield, Hart, Anderson, Considine (Lovell 79), Foster, Nicholson, Dempsey (Jamie Smith 75), Severin, Clark, Miller, Mackie. Subs Not Used: Soutar, Diamond, Touzani, Donald, Maguire.
Booked: Lovell.
Att: 58,911
Ref: D McDonald.