It was a moment to cherish for Fleck as he grabbed his first goal for Rangers to clinch a vital SPL win.
With chances few and far between and time running out, the 17-year-old starlet won a penalty 14 minutes from time and promptly slotted it home himself.
In added time Kyle Lafferty made sure of three points when he followed up after Zaluska had blocked Barry Ferguson’s effort and clipped a left foot shot into the net.
And with Celtic being held to a goal-less draw by Terry Butcher’s Inverness on Sunday, this could prove to be a huge result in the grand scheme of things.
The down side was the ankle injury to Nacho Novo which will, in all likelihood prevent him from playing against Celtic.
Dundee United have proved to be difficult opponents on most of the occasions Rangers have faced them since Walter Smith returned as manager and Saturday was no different.
The power and pace in the United ranks was quite prevalent in the early moments with the Rangers midfield struggling to get a grip of possession.
And there were some anxious moments at the back, not least in 19 minutes when Gary Kenneth’s long throw was allowed to go all the way to the middle of the box where David Robertson connected and Allan McGregor had to make a smart save.
Novo, the star of the midweek Co-operative Insurance Cup win over Falkirk, looked the liveliest from a Rangers point of view but his match was to finish three minutes before half-time.
He made a decent break in 25 minutes and hit a good pass to Kris Boyd but the Rangers striker missed the target when he tried to curl a right foot shot to the right corner.
Novo then took a knock which required treatment and when he went down again just before half-time it was clear he could not continue and Kenny Miller was sent on.
Once again Fleck was a positive for Rangers and he tested Celtic-bound keeper Lukasz Zaluska in 32 minutes with a powerful left foot drive with the Pole pushed over the top.
Of course, he was to have a huge influence later.
It was pretty tough in the early moments of the second half as Rangers found it hard to create clear opportunities.
Davis and Miller linked well in 54 minutes when the former sent the latter racing down the right then ran into the box for the return but Dods did well to intercept Miller’s low ball in.
Madjid Bougherra even popped up on the right win in 64 minutes when he cut inside Grainger and whipped over a decent cross. Boyd met it with his right boot but Zaluska made a good save.
Decisions did not seem to be going for Rangers either. The fans were raging when Kyle Lafferty – a replacement for Boyd in 74 minutes – was flagged offside a minute after coming on.
However, within 60 seconds Ibrox was rocking when Fleck won a penalty from a clumsy challenge by Mihael Kovacevic and it was a sensational moment for the 17-year-old.
He raced to grab the ball and placed it on spot showing remarkable confidence.
The bench looked on slightly apprehensively but they need not have worried as Fleck coolly slotted the ball into the left corner sending Zaluska the wrong way.
Rangers looked a relieved side and the chances really started to come their way.
Miller should have scored when Davis played him in but Zaluska made a great block and then Miller hit the rebound wide.
Lafferty had a chance at the back post but his shot was blocked.
Then he did get his moment in added time. Zaluska came running off his line to block Ferguson after Miller had played the ball through and it broke to Lafferty who directed the ball into the empty net.
Winning was the key and now Rangers have Celtic firmly in their sights.