They will be delighted to have kept a clean sheet, particularly as they had to reshuffle the defence that was on duty in last week's Scottish Cup win over Rangers.
Stanislav Varga and Didier Agathe missed out through injury, with Ulrik Laursen moving into central defence and Stephen McManus making a rare appearance at left-back. Celtic were also able to call on the services of Neil Lennon who replaced the suspended Alan Thompson in midfield.
Aberdeen boss Jimmy Calderwood will be unhappy with his side's lack of a goal threat. During the 90 minutes they were restricted to only four efforts on goal. Indeed their last SPL goal came more than four games ago in the defeat by Hibernian in early December.
Celtic created the first chance in the seventh minute. Aiden McGeady and John Hartson combined to set up Juninho but the Brazilian fired just wide from inside the area.
Celtic deservedly took the lead in the 24th minute. Hartson's aerial challenge knocked the ball wide to Stilian Petrov and he ran to the edge of the Dons area before knocking the ball into the box.
Phil McGuire failed to clear the danger and Chris Sutton pounced to slot the ball home from 16 yards, aided by a deflection off the Dons defender.
Aberdeen's response was immediate as Markus Heikkinen found the unmarked Derek Adams 30 yards out. The Dons midfielder controlled the ball before rifling in a fierce shot which was comfortably held by Robert Douglas.
Celtic threatened to double their lead on the half-hour when Aberdeen again needlessly gave away a free-kick in a dangerous situation.
From Petrov's cross into the area, Hartson got ahead of Ryan Esson but his header flew just over the bar.
Aberdeen hit back and in the 36th minute Noel Whelan timed his run to perfection as he got in behind Bobo Balde and onto the end of a clever reverse pass from Kevin McNaughton. However from an acute angle the big striker's eight-yard effort was well-held at the near post by Douglas.
With Celtic totally dominant they looked to have got a crucial second goal in the dying minutes of the half. Laursen fed the ball through to Petrov and continued his run into the Dons half.
The Celtic midfielder's precise pass found the big Dane. His run was brought to an abrupt end by Russell Anderson but the ball fell kindly to Sutton whose 14-yard effort had goal written all over it until the long legs of Alexander Diamond stretched to clear the ball off the line.
Calderwood introduced debutant Jamie Winter and Steven Tosh in place of McGuire and Adams in the 52nd minute as the Dons reverted to a 4-4-2 formation.
On the hour mark Aberdeen created their best chance of the game. Whelan and Darren Mackie combined well in midfield before the latter put Chris Clark clear.
The wide man drove into the area before neatly side-stepping two Celtic defenders as he dragged the ball back onto his right foot. His low shot appeared to strike the arm of Laursen but the referee turned aside loud home appeals for a penalty kick.
Aberdeen were at last making a game of it as Douglas had to look lively twice in quick succession to hold on to dangerous crosses into his area.
Celtic's deadly duo of Hartson and Sutton almost brought about a second goal for the visitors in the 78th minute. The Welshman cushioned a header from Jackie McNamara's cross into the path of Sutton, but under pressure from Diamond his left-foot shot from 12 yards was easily held by Esson.
Aberdeen almost snatched an unlikely point when Jamie Winter picked out Mackie wide on the left with 3 minutes remaining. The Aberdeen player waltzed past McNamara before playing an intelligent ball into the area.
The visitors' rearguard was static as Heikkinen almost got a touch but it wasn't to be as the ball ran harmlessly through to Douglas in the Celtic goal.