Yet, against an Everton side lacking conviction, Leeds had chances to take all three points, most notably in the closing minutes when Brian Deane, always their most threatening attacker, hit a post from a yard.
Leeds appeared from the start to have determined their first intention not to lose, fielding a heavily defensive formation in which Tony Yeboah, ready to resume after his long absence through injury, could be accommodated only on the substitutes' bench.
Everton were thus confronted with two wing-backs and three centre-backs in addition to Graham's man-marker, Lucas Radebe, whose duty here was to stay at the shoulder of his former Leeds team-mate Gary Speed, whose eye for goals has been sharpened by his move across the pennines.
Leeds looked the more likely to break the deadlock and twice in the first 20 minutes the home side were grateful for the alertness of Neville Southall, their veteran goalkeeper, who reacted sharply to block a snap-shot by Lee Sharpe and then scrambled to the foot of his left-hand post to save when a speculative long-range effort by David Wetherall curled menacingly on the wind.
On an icy afternoon, it was taking Everton a long time to warm up in more than one sense. But, at last, an astute pass by Tony Grant released Nicky Barmby behind the visiting defence. It was a pity Speed was not quicker to react to Barmby's pull-back. Then Ferguson, anticipating Andy Hinchcliffe's cross from the left, was foiled by a splendid tackle from Paul Beesley.
It was not until the last minute of the opening half, however, that there was real cause for excitement amongst the home crowd. Andrei Kanchelskis, fed by Barmby, cut through the Leeds rearguard with an explosive diagonal run, culminating in a stinging shot which Nigel Martyn did exceptionally well to block. A goal still looked on when the loose ball ran back to Kanchelskis but the Russian's follow-up sailed high over the bar.
By then Everton had had to replace the central defender Craig Short with David Unsworth and Leeds had to concede at half-time that Radebe was in no state to continue, sending on youngster Mark Jackson in his place.
Given that Everton considered themselves to be among the leading players in this year's Premiership it was not the most convincing performance and they lived dangerously again within two minutes of the resumption when Rush's incisive pass allowed Deane to race clear with Everton looking for an offside signal. None was forthcoming, but Deane's attempt to chip an advancing Southall was inaccurate.
All this time the Leeds supporters were clamouring for the introduction of Yeboah but Deane was posing Everton enough problems and he earned Leeds a free-kick in dangerous territory when Unsworth brought him down at the end of another positive run. Gary Kelly's free-kick, from a good 25 yards, struck the top of the crossbar.
Everton this time responded by producing their best spell. At last Ferguson began to make his presence felt in the box but, like Barmby and Speed, wasted his best opportunity by heading over the bar. Then Kanchelskis, from Ferguson's layoff, turned well to make an opening for himself but screwed his shot wide.