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Maidstone are off to Stockport in the FA Trophy quarter-finals after beating a young Salford side.
City, more concerned with promotion, made wholesale changes for the third-round replay at the Gallagher and United took advantage.
Michael Phillips quickly put them in front and Elliott Romain doubled the lead before Will De Havilland added a late third.
Stones last reached the quarter-finals in 1987, losing to Burton Albion after a replay.
Maidstone were well on top against Salford’s youngsters for much of the first half.
Romain put the wind up an inexperienced backline several times in the early stages as United flew at the visitors.
Simon Walton had a shot blocked from Ollie Muldoon’s corner and Aron Davies sent the follow-up over with a few minutes on the clock.
Romain then saw a decent hit held by Max Crocombe before United’s ninth-minute opener.
The lively Jack Powell got in down the left and played the ball across the face of goal with Phillips finishing at the far post.
Muldoon ran out of room when played in by Romain, finishing tamely, and Phillips’ header from Dan Wishart’s cross caught the outside of the post as Maidstone continued to run the show.
There was a blow for the hosts in the 36th minute when keeper Dion-Curtis Henry cleaned out player-coach Simon Walton when coming off his line for a free-kick.
It was the end of Walton’s night and he looked in some discomfort as he made his way back to the dressing room with his arm in a makeshift sling.
There was a decent chance for Salford at the end of the first half, Gus Mafuta rolling the ball just wide from Devante Redmond’s pass.
Salford had a good little spell at the start of the second half but didn’t look like scoring and Jack Paxman went close with a thumping volley at the other end, having tested Max Crocombe moments earlier.
The Stones then doubled their lead in the 59th minute, Davies with a neat ball into Romain who held off his man on the edge of the box and finished smartly in the bottom corner.
There was a little scare for Maidstone when Henry made a mess of a cross but the hosts looked comfortable and threatened a third from Powell’s 20-yard free-kick.
A superb turn and shot from Phillips followed, Crocombe getting down well to make the save.
Maidstone added their third goal in the 88th minute when a corner from substitute Jack Richards was tapped home by De Havilland at the far post.
Maidstone: Henry, Davies, De Havilland, Donnellan, Phillips, Muldoon (Richards 86mins), Walton (Tajbakhsh 41mins), Paxman (Meredith 82mins), Wishart, Powell, Romain. Subs not used: Strizovic, Swaine.
Attendance: 880.