Player-boss McAllister - taking charge of the Sky Blues for the first time in a competitive match - was indebted to substitute Gary McSheffrey, whose stunning strike five minutes before the interval was enough to secure victory.
Carl Asaba, with his first goal since February, had given United a 13th-minute lead, only for Jay Bothroyd to level matters seconds after McSheffrey's arrival on the quarter-hour-mark.
And McAllister, who capped an impressive individual performance with an assist for the equaliser, will have been delighted to see his side withstand concerted United pressure in a one-sided second half.
The game was a little more than a minute old when the first shot arrived, although Paddy Kenny in the Blades goal was not unduly troubled by Youssef Chippo's 25-yard strike.
United responded in the best fashion possible, though, Asaba turning brilliantly just outside the penalty area before firing across Morten Hyldgaard into the far corner of the net.
Coventry suffered a further setback when Laurent Delorge was forced off, but it served merely to hasten the arrival of McSheffrey and intensify the push for an equaliser.
It came within a matter of seconds, Bothroyd's header from a McAllister corner adjudged to have crossed the line following a goalmouth scramble.
McAllister was instrumental in Coventry's dominance of the opening period, with his near-post deliveries causing the Blades backline particular concern.
And the pressure told after 40 minutes, McSheffrey beating Steve Yates before unleashing a fantastic left-footed strike into the top corner.
Julian Joachim could not connect properly as Coventry went in search of a third, but they were fortunate to keep their narrow advantage when Asaba's volley from distance came back off the woodwork.
Michael Tonge attempted to follow suit with a similar audacious attempt, and Coventry were indebted to Hyldgaard just before the hour-mark, the Danish goalkeeper spectacularly tipping Peter Ndlovu's drive round the post.
Hyldgaard needed to be alert to claim a header from Shaun Murphy as United continued to push forward, with Michael Brown increasingly influential in the centre of midfield.
However, despite his sterling efforts, the Blades could not force an equaliser, and it was rather symptomatic of their second-half performance that Brown's goalbound late shot was spectacularly kept out by Hyldgaard.