However, not for the first time this season they failed to make their pressure count and they paid a heavy price as subsitute Kris Boyd scored in 86 minutes and then former Celt Tommy Johnson notched a penalty two minutes later.
The travelling fans could hardly believe it and neither could the coaching staff. Without doubt this represented McLeish’s lowest point in his short reign.
It must have been so hard to take because for the previous 85 minutes, his side had been as fluid and inventive as they have been all season.
The pace and trickery of Peter Lovenkrands has been a key element of Rangers’ play in recent matches and McLeish was keen to utilise his talents again at Rugby Park.
Dutifully, the midfield men gave the young Dane good supply early on and the ploy certainly had Killie in trouble on more than one occasion.
There were only five minutes on the clock when Tore Andre Flo’s brilliant flick sent Lovenkrands scampering down the flank. His pass looked perfect for Ronald de Boer but James Fowler made a crucial interception to concede a corner.
Then in 16 minutes Tony Vidmar hit a great pass to find the Danish youngster in a similar area and Killie were in jeopardy again. Lovenkrands eased past Fowler and then whipped over another good ball which was destined for Flo but this time Freddie Dindeleux made the interception.
Just 60 seconds later Peter hurt the Ayrshiremen again with his speed but his centre was just too strong for Shota Arveladze, who was waiting to pounce at the back post.
It was good pressure from the Ibrox men, who were being superbly marshalled in midfield by Barry Ferguson, aided and abetted by Stephen Hughes, who had come into the side in place of Bert Konterman.
Indeed it was Hughes’ excellent through ball in 27 minutes which gave Rangers another good chance. The teenager picked out de Boer on the right side of the box and he cut the ball back for Arveladze but his shot was saved by Gordon Marshall.
Rangers were well on top but Killie produced a couple of anxious moments around the hour mark which reminded the Light Blues that they still had some work to do.
Peter Canero was allowed to make a good break from midfield in 31 minutes and his shot might have troubled Stefan Klos but it hit team mate Tommy Johnson’s heel.
A might later, however, former Celt Johnson came close to having a much more positive impact a minute later when he connected with Alan McLaren’s cross from the left but his shot was just wide.
Rangers heeded the warning and by the 34th minute they had the lead, although there was more than an element of good fortune about the goal.
In fairness, the build-up was excellent. Hughes hit a brilliant pass for Lovenkrands wide on the left and although the Dane’s cross was to deep de Boer was able to retrieve.
The former Ajax and Barcelona star cut onto his left foot and let fly but the ball took a wicked deflection off Freddie Dindeleux to fly into the right corner of the net.
Rangers were worth it and they thrilled the vociferous travelling support when they went two ahead 10 minutes into the second half.
All too often when indirect freekicks are awarded inside the penalty area nothing comes of the situation but Rangers made Killie pay for a deliberate pass back by Kevin McGowne which was picked up by Marshall.
As Killie packed their goal area, Ferguson touched the ball to Amoruso and his drive was diverted into the net by Flo for his 22nd goal of the season.
The big Norwegian might have had a couple more as he was through on the keeper but in one instance he lost his balance and in the second Marshall made a brave save at his feet.
Hughes also had an opportunity to inflict further pain on Killie but in 65 minutes he shot himself when a square ball would have been more appropriate and then in 77 minutes his left foot strike was well held by the Killie keeper.
Arveladze also missed with a glaring opportunity in 71 minutes when Lovenkrands produced a perfect back post cross, heading wide from just six yards.
These misses proved to be disastrously costly as Killie pulled a goal back with four minutes remaining which made the finish far more uneasy that it might have been.
They won a freekick on the right and after the initial clearance, the ball was played back into the box where Craig Dargo headed it down and substitute Kris Boyd hammered the ball into the net with his right foot.
McLeish was furious at the concession of such a late goal but there was worse to come when Rangers, incredibly, gave away a penalty with two minutes to go to snatch a draw and stab a stick into the spokes of Rangers’ momentum in recent weeks.
It was Boyd who set up the chance with a ball into the box for Dargo and Fernando Ricksen knocked the young striker to the floor.
Ironically, it was Johnson who stepped up to take the kick and he gave Klos no chance with a well-taken spotkick to shatter the Ibrox men.
McLeish must have felt like he was mugged as the SPL gulf grew wider with Celtic winning at Livingston but his players only have themselves to blame.
KILMARNOCK: Marshall; Fowler, McGowne, Dindeleux (Hessey 72), Hay; Canero, Mahood, Mitchell, Murray (Dargo 62); McLaren (Boyd 62), Johnson. Subs not used – Meldrum, Hessey, McDonald
Bookings: McLaren (56)
RANGERS: Klos; Ricksen, Moore, Amoruso, Vidmar; Hughes, de Boer (Dodds 83), Ferguson; Arveladze, Flo, Lovenkrands (McCann 76). Subs not used – Christiansen, Ross, Caniggia.
Bookings: Moore (65) Vidmar (78) Ferguson (87)
Ref: John Underhill.
Att: 11,589.
Man of the match: Barry Ferguson
Moment of the match: Stephen Hughes’ pass for Lovenkrands in the build-up to the opening goal.