True, the impeccable McAllister did score a hat-trick: one was a cruel deflection; the second came from a fortunate free-kick and the third was a hotly disputed although coolly converted last minute penalty.
Coventry's workmanlike back line was well-marshalled by the former Leeds player David Rennie and their balanced attack of Dion Dublin, supported by the delicate pace of Peter Ndlovu and Nii Lamptey, deserved better. Indeed, the result only did justice to John Lukic's three excellent second- half saves.
Richard Jobson, Leeds's pounds 1mmidweek signing from Oldham, had to produce a couple of incisive tackles on the speeding Zimbabwean Ndlovu but only after uncomfortably clattering two of his new colleagues.
He did, though, concede the corner from which Dublin headed the opener in the 12th minute, and he should have conceded a penalty in the 33rd minute when Ndlovu fell in the area.
That was Ndlovu's last meaningful action. Minutes later he lay writhing off pitch after John Pemberton's innocuous challenge, McAllister marched into midfield and his 25-yard shot went in off Dave Busst.
Four minutes later McAllister added his second. Kevin Richardson fell on the ball and conceded a free-kick on the edge of the area and, after waiting an age while the referee Gerard Ashby paced out the 10 yards for the wall, he drifted the ball over their heads and into the goal.
The second half, though, was as ugly as Coventry's purple and yellow strip. Tony Yeboah briefly flickered into life but with Paul Telfer and Richardson running Coventry's midfield, the visitors looked more likely to score.
Leeds sneaked an 89th-minute penalty when an up and under dropped on to Marcus Hall's hand. "Somewhere along the way we have run over a black cat," the Coventry manager Ron Atkinson bemoaned. "We looked as good as a good side."
Howard Wilkinson huffed and puffed like his team to produce anything positive: "There was a disputed penalty, we've blocked things on the line, our keeper's pulled off some good saves but I'm happy to take the result." He won't be so happy on Tuesday in Eindhoven.