There were a number of stars missing for both sides with Rovers lacking their new strike duo Andy Cole and Dwight Yorke, whilst United were without Harry Kewell - who pulled out of the contest due to illness.
Rovers started the better of the two sides, with Keith Gillespie in particular causing all sorts of problems for Ian Harte down the right-hand side.
And it was the former Newcastle and Manchester United winger who created Rovers' winning goal. The Northern Ireland wide-man beat Harte to the by line, before crossing for Flitcroft to power home with the help of a slight deflection off Jonathan Woodgate.
It was no more than the Ewood Park side deserved and they really could have gone into the break with a greater lead. New signing David Thompson, who was impressive for the home side, forced Paul Robinson into an excellent save on 35 minutes.
United tried to up the tempo after the break, however the side continued to look ragged giving away possession too cheaply on numerous occasions.
However, the visitors almost equalised on 48 minutes when Nick Barmby forced Friedel into a superb save from close range, with Henning Berg clearing the rebound off the line.
With Mark Viduka looking out of sorts for Leeds, manager Terry Venables decided to roll the dice for the last time by making a triple substitution.
Venables handed Jamie McMaster his first team debut, whilst Gary Kelly and Stephen McPhail were brought on for Ian Harte and Olivier Dacourt.
Just minutes after Harte was taken off, Leeds were awarded a penalty by Graham Poll when Berg handled Barmby's cross in the penalty area.
However, Leeds failed to capitalise when Smith unconvincingly stepped up and fired his shot into the grateful arms of the American keeper.
Despite late pressure by the visitors, Rovers held on for a thoroughly-deserved win and could even have extended their lead - with United pushing forward searching for that elusive equaliser.
