Town made one change from last week’s line up, with skipper, Josh Falkingham, returning to replace the injured George Thomson.
Town were first into the attack and a Ryan Fallowfield run and pass found Kiernan, who tested Jordan Holmes with a powerful cross shot.
Fleet began to make their presence felt and James Belshaw had to move smartly off his line to snatch Myles Weston’s dangerous centre away from Alex Reid.
The visitors were having plenty of possession without posing much of a threat to Town, although Will Smith had to make a vital clearance from Weston and Reid shot over the angle of post and bar.
However, Town began to gain the upper hand and Fallowfield forced Holmes to save at the foot of the near post.
Town’s opener arrived five minutes before the break when Falkingham’s header was flicked on to Alex Bradley by Mark Beck and the midfielder’s measured pass enabled Kiernan to round Holmes and slot into the net.
Fleet started the second half on the front foot and Chigozie Ugwu had a shot diverted for a corner, before soon afterwards, forcing Belshaw to tip a rising drive over the bar.
Frankie Sutherland, then hit a flashing drive from 25 yards just wide of the upright,but that was as good as it got for Fleet.
Jack Muldoon shot into the side netting after being played in by Falkingham’s pass,but with twenty minutes left, Kiernan made the game safe for Town.
Muldoon picked out the overlapping Fallowfield and his diverted centre was headed past Holmes by Kiernan from close range.
So its on to Wrexham on Tuesday evening, when Town hope to extend their unbeaten run to six games.
Att.742 (inc 47 away)
Belshaw,Fallowfield,G Smith,Burrell,W Smith,Hall,Falkingham,Kiernan(Diamond 85),Beck,Muldoon,Bradley.
Unused subs, Emmett,Brown,Stead,Cracknell.
Scorer,Kiernan 40,59. Man of the Match, Kiernan.
Holmes,King,Wilson,Weston,Grimes,Egan(Adelove 67)Cordner,Sutherland(Obileye 78),Ugwu,Reid,Payne.
Unused subs,Palmer,Achuba,Biabi. Att.742(inc 47 away)