But when the action got underway, it was the visitors who showed more prowess in front of goal as a Georgios Samaras double settled the contest.
The final result means Gers are now four points off the pace in the title race, although they do still have two games in hand over their Old Firm rivals.
As is increasingly the case in high-profile matches, Walter Smith sprung a surprise with his team selection by giving another youngster a full first-team debut.
In the first derby at Ibrox last season, Andrew Little was a shock choice at right-back and Kyle Hutton came in to play in central midfield against Manchester United in November.
On this occasion it was Jamie Ness, so impressive in his short cameo against Motherwell on Boxing Day, who joined Lee McCulloch in the engine room.
He came in as a replacement for Steven Naismith, who failed to shake off a hamstring injury sustained against the Steelmen.
But Steven Davis did recover enough from a similar problem to slot in on the right side of midfield, with Steven Whittaker moving across to the left.
Vladimir Weiss was deployed in the hole behind lone striker Kenny Miller as Gers tried to press their opponents from the off.
For the visitors, there was no Freddie Ljungberg as a virus sidelined him after he moved to Parkhead earlier in the week.
Before the match began, the sides were led out on to the pitch by the two club captains in 1971, John Greig and Billy McNeill.
An impeccably-observed minute’s silence then followed as everyone in the stadium paid tribute to the victims of four decades ago.
The emotional period of remembrance made for a highly-charged atmosphere as play got underway and it was Rangers who made most of the early running.
They had the first chance too on five minutes as Weiss swung a corner in and McCulloch headed goalwards only to see his effort nodded on to the bar by Emilio Izaguirre.
Whittaker fired the rebound well over after it was inadequately cleared, before Weiss did the same thing moments later.
Ness was settling well and his pinpoint cross-field passing was creating all sorts of openings for the hosts.
But they couldn’t make any of them count, even if Celtic didn’t really look like they knew how to deal with the home team’s attacking threat initially.
Although the away side was sitting back for much of the opening exchanges, they were also restricting Gers to shots from distance.
And after another neat piece of play from Ness, McCulloch rifled well over the upright from 25 yards.
Having had the bulk of the ball to begin with, the Light Blues were starting to be pegged back a little as Celtic settled.
Allan McGregor had to be alert to punch one dangerous corner away then it took a stunning last-gasp McCulloch tackle to deny James Forrest.
Rangers knew they had to up the ante again but with half an hour gone, it was Neil Lennon’s men who were imposing themselves more.
Whittaker tried to temper that when he got on the end of a deep Weiss cross but he got his timing all wrong and screwed past the post.
The first half was ending with a whimper and with no injury time to be added, referee Craig Thomson blew for the interval to muted applause.
You sensed Lennon would have been happier with the way things had panned out than Smith as the players trooped towards the tunnel for their team talks.
But whatever was said in the home dressing room was almost rendered redundant seconds after the restart as Paddy McCourt was played in and only just shot wide.
Bougherra then sliced a good Charlie Mulgrew free kick behind as Gers hung on to parity and the away team grew in confidence.
The game continued to trundle along with gathering any momentum and it was taking the Ibrox team some time to find its feet.
But then, just after the hour mark, Celtic took the lead – and the goal was largely Rangers’ doing.
A long ball over the top of the defence caught out David Weir and Bougherra, with Samaras beating them to it.
He still had a lot to do but McGregor made a late decision to come racing from his goal and when the Greek got there first, he rounded the keeper then slotted in.
Celtic’s 4-5-1 shape had really restricted Rangers and now that the visitors had a lead, Smith’s players had it all to do.
Frustration was certainly kicking in and it wasn’t a great surprise to see Richard Foster taken off and replaced by Kyle Lafferty.
But things soon went from bad to worse as the Parkhead team charged straight upfield and won a penalty when Samaras went down under Bougherra’s challenge inside the box.
The striker then stepped up himself to stroke into McGregor’s left-hand corner and although the keeper went the right way, he still couldn’t reach it.
Sasa Papac almost pulled a goal back when he connected with a Weiss corner but his volley whistled inches beyond the woodwork.
Bougherra also turned the ball over when Whittaker dinked into the mix as Rangers finally started to ask questions of the away back line.
Davis had a go when Weiss was fouled as he surged forward but although he came as close as any home player had to scoring, he was still off target.
The minutes were beginning to tick down and as Celtic started to eek every second out of each, it was very quickly becoming clear this wasn’t to be their day.
And when Thomson signalled for full-time, it brought to an end a disappointing day that Gers will look to bounce back from when Kilmarnock visit Ibrox next Monday.