New Pools boss Matthew Bates saw his side struggle to take control early on, with a half chance for Padraig Amond all they had to show for the first 25 minutes at Victoria Park.
Dover, who are adjusting to life without 40-goal marksman Ricky Miller, then took the lead after 29 minutes through debutant Jamie Allen. The ex-Southport striker turned sharply to find space in the box and curl home amid a scramble from a corner.
Amond continued to threaten for the hosts, but Kane Richards missed a gilt-edged chance to put the visitors 2-0 up after 55 minutes and then Ryan Bird headed just wide in the closing moments to leave Pools in no doubt that getting back up will not be easy.
Match report supplied by the Press Association.
Match ends, Hartlepool United 0, Dover Athletic 1.
Second Half ends, Hartlepool United 0, Dover Athletic 1.
Scott Harrison (Hartlepool United) is shown the yellow card.
Substitution, Dover Athletic. Kadell Daniel replaces Kane Richards.
Substitution, Hartlepool United. Nicky Deverdics replaces Lewis Hawkins.
Substitution, Dover Athletic. Mitchell Pinnock replaces Nortei Nortey.
Liam Donnelly (Hartlepool United) is shown the yellow card.
Substitution, Hartlepool United. Rhys Oates replaces Jack Munns.
Substitution, Hartlepool United. Jake Cassidy replaces Michael Woods.
Second Half begins Hartlepool United 0, Dover Athletic 1.
First Half ends, Hartlepool United 0, Dover Athletic 1.
Goal!  Hartlepool United 0, Dover Athletic 1. Jamie Allen (Dover Athletic).
First Half begins.
Lineups are announced and players are warming up.
Hartlepool fell to a 1-0 defeat against Dover in their first clash after being relegated from the Football League last season.