Inspired by Lorenzo Amoruso and two-goal Shota Arveladze, Rangers were made to sweat by poor defending which allowed United two goals and this is a situation McLeish will clearly have to address.
However, it all ended up the right way for the new boss and his players but he was given further evidence of the task he has on his hands at Ibrox.
Finally, McLeish got to meet his public as he was introduced to a roaring reception before kick-off. The fans lapped it up as he bowed to each stand and McLeish undoubtedly savoured the moment.
As announced, Simply The Best came back and the fans respected the club’s wishes by singing the proper words but it is what happens on the field which is most important for McLeish and he was delighted to see his new charges go ahead in the game.
Rangers started the game well, moving the ball sweetly as they have been doing in most of this season’s matches. However, there was a lack of a cutting edge, just as there has been so often this season.
United were forced to run around but it was the Tannadice side who had the first shot on target. Former Rangers winger Stephen Carson’s freekick was only cleared as far as David Partridge in 10 minutes and he drove a left foot shot from 25 yards but Stefan Klos had it covered.
It must have alarmed McLeish a little and the move certainly gave United encouragement. They had some good moments as Rangers were forced onto the defensive.
However, Ronald de Boer and Shot Arveladze eased the tension when they combined to devastating effect in 20 minutes to give Rangers the lead.
Dutchman de Boer won the ball in his own half and burst forward, catching United on their heels a little. Arveladze then got off his mark and de Boer clipped a perfect left foot pass between Jamie McCunnie and Danny Griffin to release the Georgian striker.
Shota was through on Paul Gallacher and showed tremendous coolness as he slammed a left foot shot past the young keeper to claim his 10th goal in a Rangers shirt.
The crowd were entitled to feel that the strike would settle things down, but there was further evidence of the work McLeish has to do when Rangers lost a goal from a set piece in 28 minutes.
United won a corner on the left side and Carson whipped it over. The ball was only half-cleared allowing Jim Lauchlan a strike at goal and his left foot shot smacked off the face of the crossbar.
United’s aggressive young striker Stephen Thompson was the quickest to react and sent a downward header into the Rangers net.
The Bears were not best pleased – especially as Rangers looked a bit rocky for the next five minutes. Gradually, the Ibrox men began to reassert themselves and they came close when Gallacher could only palm away Ricksen’s cross in 36 minutes but the ball dropped just behind Arthur Numan.
Then a minute later Numan played in Arveladze with a lovely outside of the boot pass but the former Ajax man fired his shot into the side netting from a tight angle.
It took the inspirational Amoruso to sort things out with his first league goal of the season in 42 minutes and boy did he celebrate.
Mo Ross won a corner on the right, Ricksen drove the ball over and Amoruiso rose above everyone to power a header into the left corner. He then set off on a victory run towards the Rangers dugout and hugged assistant boss Andy Watson.
The whole situation looked even rosier when the two best players on the park combined to give Rangers a 3-1 lead in 54 minutes and McLeish must have thought there and then that the game was over.
Amoruso hit a superb diagonal ball from just about halfway to release Arveladze on the left side and United were completely exposed. Lauchlan deliberated blocked Ricksen as he tried to get into the box to give Arveladze a target and it was a challenge which merited a booking.
However, Shota did not need him. He drove into the box, eased past McCunnie and slammed a right foot shat past Gallacher.
The emotional rollercoaster had not ended its journey, however, as Rangers lost a terrible goal just two minutes later and the blame lies squarely on the shoulders of Tony Vidmar.
The Aussie defender completely lost Thompson in the box as Carson played in a cross from the left side and the other Rangers defenders looked on in horror when they saw how much space the United striker had.
In keeping with his excellent performance, Thompson took the ball down and drilled a left foot shot past a very angry Klos.
It meant that although Rangers were still ahead they virtually had to try to win the game all over again to disabuse United of any notion of a revival.
It looked as though they had achieved this aim in 64 minutes, but somehow Gallacher kept United in the game.
Ross got to the goal-line and drove over a low cross. De Boer cleverly dummied it, Flo somehow missed it and then Gallacher blocked Arveladze’s shot with his right boot. United only cleared the ball as far as Numan and he hammered a left foot shot which the United keeper brilliantly blocked.
McLeish brought on Claudio Caniggia to try and force the issue and he undoubtedly made a difference with his pace and trickery but it was still nervous for the last 20 minutes.
Caniggia regularly got behind the United defence and produced excellent crosses but no-one seemed to get on the end of them.
Indeed there was a horrifying moment when former Ranger Charlie Miller cut the ball square for substitute Ronnie O’Brien with three minutes remaining and it seemed a certain goal but the youngster on loan from Juventus contrived to lose his cool and Rangers survived.
In the end Ranger had done enough. It was hardly emphatic, but it was a highly welcome win for McLeish and his players.
RANGERS: Klos; Ross, Amoruso, Vidmar; Ricksen, Konterman, Ferguson, Numan; de Boer, Flo (Caniggia 72), Arveladze. Subs not used – Dodds, Wilson, Christiansen, Lovenkrands.
Bookings: None
DUNDE UNITED: Gallacher; McCunnie, Griffin, Lauchlan, Partridge: Carson (Hannah 59), Miller, Easton, Venetis (O’Brien 70), Paterson (McConalogue 83); Thompson. Subs not used – Combe, Hamilton.
Bookings: Thompson (42)
Ref: Kenny Clark
Att: 47,315
Man of the match: Lorenzo Amoruso – just shaded it from Arveladze.
Moment of the match: Amo’s super pass to set up Shota for the third goal.