Ronald de Boer looped the ball over the Celtic defence and as Caniggia tried to chip the out-rushing Douglas he put his shot just wide of the right hand post.
As the Light Blues mounted another attack the visitors conceded a corner and Amoruso should have done better with his header as he rose unmarked, but put it over the bar.
In only the ninth minute O’Neill was dealt a harsh blow when Rab Douglas was forced to come off with an injury to be replaced by Javier Sanchez Broto.
And he was called into action almost immediately when Peter Lovenkrands was body-checked on the edge of the box, before Ferguson was fouled by Valgaeren as Dallas waved played on.
The game was stopped and the young Dane was given immediate medical attention as he writhed around in considerable pain.
Ferguson curled the resultant free kick and when the ball broke from the Celtic wall at de Boer’s feet he really should have done better than to put it past the post from 10 yards.
In the 17th minute Didier Agathe was booked for another tackle on Lovenkrands but Amo’s driving free kick was charged down.
Ten minutes later Jackie McNamara nearly enjoyed some good fortune when he sent a 40-yard ball into the box and when no one cleared, it rolled through to bounce off Klos’ right hand post.
It was to be a warning that the Light Blues should have paid more attention to though and mid way through the half Celtic took the lead.
In the 27th minute Lorenzo Amoruso stuck a leg out and caught John Hartson just inside the box and Hugh Dallas had no hesitation in pointing to the spot.
Allan Thompson stepped up and sent Stefan Klos the wrong way to give O’Neill’s men ahead.
Five minutes later Henrik Larsson nearly doubled their tally but Craig Moore did brilliantly to head the Swede’s curling shot over the bar.
It was only a matter of time, however and just before the break John Hartson did add a second. Agathe broke quickly down the right and when Larsson dummied his low cross in to the box Hartson hammered it past Klos.
It certainly wasn’t the first half Alex McLeish had hoped for and there were a few choice words said in the dressing room at the break.
Having only recently recovered from a hamstring injury Mikel Arteta started on the bench but was called upon at half time to replace Bert Konterman.
After missing the last Old Firm game at Ibrox with a similar injury the young Spaniard looked particularly fired up in the opening minutes of the second spell and alongside Ferguson the midfield had more purpose going forward.
In the 54th minute Ricksen took control from the right and after playing a one-two with de Boer on the edge of the Celtic box hit his shot just wide.
60 seconds later Mikel Arteta whipped in a fierce corner and once again Amoruso rose above everyone but headed wide.
The signs were looking good for Gers now and in the 57th minute Arthur Numan delivered an excellent ball into the box from the left and Ronald de Boer was on hand to head past Broto.
The Light Blue revival had started and as the sun emerged from behind the clouds over Ibrox it seemed an equaliser was just on the horizon.
Some clever play by Caniggia on the right tricked Laursen and although the hitman’s cross dropped to de Boer he couldn’t curl it enough to beat Broto.
Both Amoruso and Arteta came close with long-range free kicks but both times Celtic managed to clear.
The Light Blues were given another warning though as Larsson glanced Thompson’s corner just past the post and McLeish decided another change was needed.
Neil McCann came on for Caniggia and Lovenkrands swapped to the right side of attack to make way for the Scotland international.
Despite their game mid-week Celtic were still battling hard and Stefan Klos made an excellent save in the 75th minute to deny Larsson, when he stopped a certain goal-bound strike with his foot.
It was the last throw of the dice as the manager threw on Steven Thompson to replace Peter Lovenkrands.
In the 90th minute and in a pathetic attempt to waste time, Broto punched the ball away after Celtic were awarded a goal kick and deservedly was given a yellow card by Dallas.
The visitors were solid at the back, however and the work they did in the first half was enough to see them through the match.
The points difference is now back to five points, with a game in hand for Celtic, and the title race is once again right open.
RANGERS: Klos, Ricksen, Moore, Amoruso, Numan, Konterman (Arteta 45), Ferguson, de Boer, Caniggia (McCann 71), Mols, Lovenkrands (Thompson 81)
Unused Subs: McGregor, Ross
Bookings: Lovenkrands, Moore, de Boer
CELTIC: Douglas (Broto 9), Valgaeren, Balde, Laursen, Agathe, Lennon, McNamara, Thompson, Sutton, Hartson (Petrov 65), Larsson.
Unused Subs: Maloney, Smith, Crainey
Bookings: Agathe, Hartson, Lennon, Sutton, Broto
Referee: Hugh Dallas