The Italian defender pounced from close range just as it seemed Warren Joyce's side would be denied victory in front of a healthy crowd at Langtree Park.
United, missing Ryan Tunnicliffe and Reece Brown following their loan moves to Barnsley and Ipswich Town respectively, had more than held their own against a strong Liverpool team featuring the likes of Raheem Sterling, Jonjo Shelvey and Andre Wisdom.
But the visitors almost failed to capitalise on the dismissal of Liverpool defender Stephen Sama early in the second period, spurning several presentable chances to score before Fornasier's late intervention.
Jeffery Schlupp impressed as a lone striker for United on the first competitive outing of his spell on trial from Leicester City, while the Reds also fielded Alex Büttner and Nick Powell, the latter back in central midfield after his recent stint up front.
Schlupp, who has won full international honours with Ghana, troubled Liverpool all night with his pace and could have scored several times in either half.
Inside two minutes, the 20-year-old slotted just wide after racing onto a through-ball and, soon after, saw his shot blocked by Liverpool goalkeeper Daniel Ward after being played through by Tom Lawrence.
United had started brightly and, 10 minutes before the break, Ward was again called into action to deny Schlupp after a surging run by