Victory put Pools, who went in the Easter weekend in the drop zone, four points clear of fourth-bottom Tranmere.
But the visitors, with one of the division's best away records, started the brighter. Scott Flinders had to keep out a Seb Carole header after just three minutes and, with the home side struggling to cope with Albion's neat passing game, the first-half was a non-event.
But the opener arrived after 54 minutes when Armann Bjornsson chested the ball into the path of Leon McSweeney who played into space for O'Donovan to race onto and superbly clip past keeper Peter Brezovan from the tightest of angles.
Ashley Barnes glanced a header wide for Brighton, but Pools were soon two goals to the good. James Brown sprayed the ball wide to Andy Monkhouse who cut in from the right wing and curled his shot across Brezovan and into the far corner.
Flinders saved twice from Inigo Calderson and touched Gary Dicker's curler against the bar two minutes from time.