Celtic 3 Rangers 0
The hosts may only have had four efforts on goal but the difference was that three of them counted.
John Hartson gave the home side an early lead and goals from Bobo Balde and Aiden McGeady in a five-minute spell just before the hour-mark finished the match as a contest.
The home side were then content to knock the ball about as Rangers ran out of ideas.
To add to the visitors' worries Dado Prso limped off midway through the second half and must be doubtful for their Champions League match against FC Porto in midweek.
On this form Rangers will struggle to qualify for a UEFA Cup place at the end of this season.
Sotirios Kyrgiakos conceded an early free-kick and Shunsuke Nakamura's in-swinging cross was missed by everyone as it drifted past Ronald Waterreus, with the Dutchman preferred in goal to Stefan Klos.
Rangers replied with a cross from Fernando Ricksen but Hamed Namouchi failed to make a decent contact with his first-time strike.
It was a bright opening to the match and the Gers certainly looked as if they were going to make more of a fight of it than they did in the recent CIS Cup quarter-final meeting between the sides.
Mo Camara lost possession but although Francis Jeffers controlled the ball well, his shot was always rising and cleared the crossbar.
Rangers received more encouragement when Alan Hutton's cross found Namouchi, only for the Tunisian to head weakly at home keeper Artur Boruc.
However, Rangers lost the early momentum when a wayward pass from Hutton gifted possession to Celtic and led to the opening goal.
Nakamura seized on the loose ball before releasing the unmarked Shaun Maloney down the right wing. The striker's cross was clinically side-footed home by Hartson with the Rangers defence caught cold.
The visitors should have equalised six minutes later when a superb cross by Barry Ferguson found Namouchi unmarked, but from only six yards the midfielder headed wide. It was to prove a costly miss as Rangers desperately strived for an equaliser.
Kyrgiakos then wanted too much time when a Ferguson free-kick fell to him in the penalty area and the chance was lost.
Gordon Strachan's men were content to strike on the counter-attack and from one break McGeady's pass was just intercepted by Marvin Andrews.
Rangers' lack of confidence was shown when Prso snatched his shot from Kyrgiakos' long ball, with his effort ending high in the stands.
Boruc then came to Celtic's rescue when he timed his dive perfectly to gather the ball from Ferguson's feet as Stephen McManus was caught out of position.
The visitors had created more chances than Celtic in the first half but still went in one behind at the interval.
Early in the second half Andrews committed a crude tackle from behind on Maloney and was correctly booked. It looked bad for the Celtic player when he was stretchered off, but fortunately he made a quick recovery, though he was substituted shortly after Celtic took a two-goal lead.
Before that goal, Celtic had to survive a strong claim for a penalty when Paul Telfer clearly handled Namouchi's flick, but the referee was content to award a corner.
Then, from a move flowing the length of the park, Hartson was only denied by a last-ditch tackle from Ricksen. However, Celtic's second goal was not long delayed as they scored from the resulting corner.
From a short corner Nakamura twisted one way and then another, before curling a great cross to the near post which Balde glanced home with his head.
Waterreus was helpless for that goal, but the visiting shot-stopper was certainly at fault for the Bhoys' third.
McGeady managed to get a touch to Stilian Petrov's cross but his effort appeared to lack power, until the Rangers keeper let it slip from his grasp and it rolled into the net.