Former Everton ace Cadamarteri glanced in Frank Sinclair's cross from the left on 12 minutes to score his third goal for Town.
Cadamarteri, who has also played for a string of Yorkshire clubs including Bradford, then set up substitute Luke Beckett for the clincher three minutes from time.
Boss Andy Ritchie had been under pressure from chairman Ken Davey to improve results and performances after Town leaked 27 goals in all competitions so far this season.
But centre-backs David Mirfin and Nathan Clarke both had a commanding games for Town and successfully snuffed out Hartlepool's threat.
Richie Barker's sixth minute shot, deflected into the sidenetting by Mirfin, was as close as Hartlepool went all night and was a classic example of Town's improved defending.
The Terriers, who had only won once in nine games before Saturdays 3-1 win over Port Vale, were a constant threat up front.
Veteran frontman Andy Booth headed just over from Clarke's cross on 18 minutes and was then denied a goal in the second half when his shot was blocked by Hartlepool keeper Jan Budtz's legs.
Budtz then made a great double save from Booth and Mirfin on 61 minutes, after Cadamarteri's initial shot deflected of Gary Liddle and caused a goalmouth scramble.
Ronnie Wallwork, on loan from West Brom, tested Budtz on 67 minutes with a stinging drive from 30 yards.
Budtz did well to hold on to the effort and just before Beckett sealed the win he also parried a shot from Andy Holdsworth.
Hartlepool had their fare share of possession in the second half, but failed to test the Terriers keeper Matt Glennon with even one shot on target.