The first Old Firm clash of the season ended in triumph for Celtic after a stunning late strike from midfielder Alan Thompson.
Celtic's Alan Thompson wheels away after scoring his side's winner
Martin O'Neill's side landed their seventh consecutive win over Rangers after a tense and cagey encounter.
Celtic's new signing Juninho looked impressive on his debut, unsettling the Ibrox side with his direct running.
But it was Thompson who was the hero after his 85th minute goal gave victory to the hosts.
Alex McLeish opted to leave Peter Lovenkrands and Stephen Hughes on the bench, with youngster Alan Hutton getting a start at right back.
Alex Rae made his Old Firm debut alongside Fernando Ricksen who was operating in midfield.
Celtic lined up without striker Chris Sutton, but Martin O'Neill handed new signing Juninho his first Celtic Park start.
Neither side looked threatening in a disappointing first half, with Celtic enjoying the bulk of possession and creating more goal-scoring opportunities.
Brazilian playmaker Juninho grew into the game as the half wore on, making some penetrating darts upfield, worrying the Rangers defence with his pace.
It was the diminutive midfielder who came closest to breaking the deadlock.
In the final minute of the opening half, he saw Klos off his line and attempted a chip over the German keeper, but the ball landed harmlessly on top of the net.
Rangers could have opened the scoring as early as the first minute, when Nacho Novo sent Prso clear, but Didier Agathe tracked back and slid in to take ball from under his feet.
Alex Rae then sent Novo clear on six minutes, but again Agathe was on hand to head off the danger with a well-timed sliding tackle on the edge of the box.
Rangers hit back as Shota Arveladze struck a left-footed shot after 30 minutes, but the Georgian's attempt went wide of David Marshall's left hand post.
Juninho made another darting run and jink into the box on 32 minutes, but his shot was deflected out for a corner.
The former Middlesbrough ace was then involved in a minor dust-up with Rae in the box, but referee Hugh Dallas let the incident pass.
The hosts had a chance within a minute of the re-start when Henri Camara whipped a ball across the face of goal, but neither Juninho or John Hartson could latch onto it.
Hartson had a clear chance on 59 minutes when he leapt to connect with a McNamara corner, but the Welshman nodded straight into the arms of Klos.
O'Neill introduced Ross Wallace in the 64th minute, taking off a busy but ineffectual Camara.
Prso had a great chance on 71 minutes after a strong Alan Hutton run, but the Croatian's shot from the edge of the box was blocked by David Marshall.
Celtic broke the deadlock in the 85th minute after Alan Thompson blasted in an unstoppable drive from the left hand edge of the penalty box which dipped over a helpless Klos.
Rangers ended the game pushing for an equaliser, but Martin O'Neill's men held on to take the three points.
Celtic: Marshall, Agathe, Balde, Varga, McNamara, Juninho (Valgaeren 87), Lennon, Petrov, Thompson, Camara (Wallace 64), Hartson (Sylla 84).
Subs Not Used: Douglas, Pearson, McGeady, Cuthbert.
Goals: Thompson 85.
Rangers: Klos, Hutton, Boumsong, Moore, Vignal, Ricksen, Mladenovic, (Thompson 87), Alex Rae, Arveladze (Lovenkrands 53), Prso, Novo.
Subs Not Used: Graeme Smith, Burke, McCormack, Andrews, Hughes.]
Booked: Moore, Alex Rae.
Ref: H Dallas (Scotland).