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Dan Sweeney scored his first Maidstone goal in a 2-0 win at Bath City on Saturday.
Sweeney - the only change from United’s win over Margate - put the visitors in front in just the third minute.
Jay Saunders' men then defended superbly before late substitute Jay May clinched one of their best results of the season.
Second-placed Stones are now only six points behind National South leaders Ebbsfleet.
Sweeney and Charles Banya combined smartly down the left to win the corner which led to the opening goal.
Karagiannis’ inswinger was fisted clear by Steve Phillips but the ball was soon back with the Greek winger, whose cross was headed in by Sweeney at the back post.
A mistake by Frankie Artus midway inside his own half presented possession to Sweeney soon after, with Phillips clinging on to a zipping low drive at the second attempt.
City’s main threat came from wing-backs Dan Bowman and Danny Greenslade, bombing forward at every opportunity and testing the Stones defence who stood up well.
City started to enjoy more of the ball but were forced into misplaced passes by a Stones outfit who didn’t give them a moment’s peace, starting in attack with Alex Akrofi hassling the centre-halves.
Bath looked nervous whenever Maidstone broke and got Karagiannis in crossing positions but it was mainly the hosts on the front foot with Lee Worgan saving from Greenslade and then, from close range, Ashley Kington.
The Stones captain also did well after big striker Nick McCootie made room on the edge of the box.
Worgan came to the rescue after a mix-up involving James Rogers late in the half while when Bath broke quickly from a Maidstone corner, winger Banya was back with a clearing header - typifying the visitors’ workrate.
Stones had a big chance to double their lead early in the second half.
Bath were screaming for a free-kick after Joe Healy slid in on dangerman Bowman but the referee waved play on and Banya launched a terrific run down the left before crossing for Akrofi whose near-post strike was blocked for a corner.
McCootie was inches away from equalising at the other end after a free-kick dropped in the box as Bath pressure mounted in pouring rain.
It was attack v defence by the midway point of the second half, Stones continuing to work hard to close the door and limiting Artus to a strike from outside the box.
The ball somehow stayed out when substitute Chas Hemmings got his head to a corner but having been on the back foot Stones suddenly found themselves two up.
The goal came on 77 minutes, Callum Driver nicking possession down the right and laying on a tap-in for May.
Stones’ second goal knocked the life out of Bath and it took an excellent block to deny the visitors a third after May played in Bobby-Joe Taylor.
Maidstone: Worgan, Driver, Mills, Coyle, Davies, Rogers, Banya (Taylor 80mins), Healy, Akrofi (May 68mins), Sweeney, Karagiannis (Bodkin 76mins). Subs not used: Parry, Paxman.
Attendance: 710.