Wright, who returned to the club for his third stint as manager, saw his side fall two behind, with goals from Craig Stanley and a penalty by Rene Howe, before a spirited fightback saw the visitors hanging on for victory as both sides ended the game with ten men.
The visitors went ahead in the 32nd minute through Craig Stanley. Stewart Drummond's pass was cleverly dummied by Howe, allowing Stanley to latch onto the ball and slot it past keeper John Danby with a cool side-footed finish.
Chester wasted a great opportunity to level matters seven minutes into the second period when Eddie Johnson was sent clear by Jay Harris, but the forward delayed his shot, allowing Henry McStay to get a vital touch on the effort which deflected wide for a corner.
The advantage was doubled on 56 minutes after a rash challenge by Laurence Wilson on Carlton gifted the visitors a penalty. The spot- kick was dispatched by Howe despite Danby going the right way.
The home side gave themselves hope with a goal on the hour mark through Johnson, who scored his first goal for the club with a downward header into the bottom corner after a great cross by Wilson.
Curiously, Johnson's 'reward' for scoring was to be substituted almost immediately as he was replaced by Paul Rutherford.
Chester should have drawn level when a great run from Wilson saw him cross to Lowe who was unmarked and in front of goal, but the striker mis-controlled the admittedly difficult ball, and the chance was gone.
Roche also produced a brilliant save late on to tip aside a stinging shot from Lowe which had been destined for the back of the net, and Kevin Ellison and Danny Adams were both dismissed eight minutes from time following the Chester striker's high challenge on Fraser McLachlan which caused a scuffle on the halfway line.