Paul Peschisolido claimed the match ball after his first ever hat-trick for United paved the way for this impressive victory.
It helped make up for the loss of injured Dean Sturridge and suspended Ashley Ward, and he was the difference between the two sides on the night.
His treble came in the space of 28 minutes either side of half time, after United survived a typical Gillingham start, which kept goalkeeper Paddy Kenny busy. He kept out efforts by Mamady Sidibe, debut-boy Darius Henderson and Chris Hope.
United finally found their feet and began to dominate with Jack Lester and Peschisolido going close.
Henderson, signed from Reading on the eve of the FA Cup tie against Charlton tried hard to impress. He had a great chance to celebrate his first goal but headed wide from Danny Spiller's cross.
Then Spiller himself, so impressive against Charlton, produced a superb 30-yard strike that crashed off the bar with Kenny rooted to the sport.
However, three minutes later Peschisolido broke the deadlock with a typical striker's goal. A long kick by Kenny was helped on by Allison and the little Canadian jinked his way into the box to fire past Nico Vaesen.
Peschisolido's contribution proved the difference between the two sides. He might not have been in the starting line up had other players been available but he certainly proved Neil Warnock correct to select him alongside Allison, with Lester playing behind the front two.
Defender Phil Jagielka set up the second on 58 minutes. His cross was headed down by Michael Tonge for Peschisolido, the smallest striker on the pitch to stoop forward and convert.
Eight minutes later he got the third, firing home from a narrow angle, having moments earlier needed treatment following a challenge by John Hills.
The third goal capped United's victory but they could have got a fourth.
Lester hit a post and then Peschisolido laid on another chance only for Vaesen to pull off a good save.
Warnock confirmed that Paul Shaw is set to complete his move to Bramall Lane in a Â£75,000 deal between the clubs on Monday.
Meanwhile, Hessenthaler continues to search for additions to his squad with Sidibe now on African Cup of Nations duty with Mali.