Aaron Capon was the star of the show with a clinical performance as he struck his first hat-trick for the club, while Liam Baitup struck twice as United bounced back from Saturday's FA Cup exit in the best possible way.
United came close to taking the lead in the opening minute as Dom Clarke and Ryan Cooper were denied following a corner, but Capon opened the scoring after just three minutes to open his account for the evening as he raced onto an inch perfect through ball from Liam Painter to confidently finish past former United 'keeper Mateusz Szafranski.
The lead was doubled soon after as Baitup sent Szafranski the wrong way from the penalty spot.
St Francis were determined to make a game of things as Jeffrey Mahadoo tested Callum Christie with a half volley from 12 yards that the United stopper turned around the post.
At the other end, Szafranski pulled off a superb stop to deny Dom Clarke from close range as United went in search of a third goal.
The third goal arrived five minutes before half time as Capon added to his tally when he guided Zak Dove's whipped free kick into the back of the net.
United carried on in the same vein during the second half as Baitup doubled his tally following another through ball from Painter, as he rounded Szafranski and rolled the ball into the net.
The fingertips of Szafranski denied Baitup a second hat-trick of the season while Jamie Bunn saw an effort curl off the far post and into the grateful arms of the visiting 'keeper.
But the night belonged to Capon as he completed his treble with four minutes remaining as he raced on to a lofted pass to slot home and seal a successful evening for United