After away wins at Mansfield and Sheffield United in the past week, Colin Cooper's side made it a hat-trick against an Exeter side who started the day third in the League Two table.
Jack Baldwin opened the scoring when he glanced in Jack Compton's cross after 21 minutes before Luke James made it two-nil five minutes after half-time with a brilliant second, taking down Compton's fine pass and lofting the ball expertly over the head of Artur Krysiak.
Compton crowned a superb individual performance - and all-round team showing - with the third when he capitalised on more hesitant Exeter defending to lash the ball home after 62 minutes.
Exeter were dreadful and it took until the 88th minute before they registered an effort on target but Scot Bennett's header was easy for Scott Flinders.
It was meant to be a day of celebration for the Grecians, who marked 10 years of Supporters' Trust ownership, but there was nothing to cheer with Hartlepool deserving and impressive winners.