Keshi Anderson gave the Tangerines an eighth-minute lead as the second-tier visitors had a number of chances.
David Ferguson levelled for Pools against his former club before teenager Joe Grey won it for the fourth-tier outfit just after the hour mark.
Story of the match
Tom Crawford came close to giving Hartlepool the lead as his free-kick glanced off the wall and a subsequent overhead kick by Gavan Holohan was fired wide.
Hartlepool failed to clear and despite Gary Liddle attempting to clear off the line, Anderson beat Killip in the bottom corner.
Four minutes later, the Tangerines thought they had doubled their lead after a fine cross found Callum Connolly, but the flag was up for offsides.
Shane Lavery went just wide and Ferguson was forced to clear off the line from a Marine header as Blackpool continued to push for a second.
Hartlepool had half-chances, Nicky Featherstone floating a free kick wide and Dan Grimshaw held a Ferguson free kick.
In stoppage time, Lavery sent a cross from substitute C.J. Anderson over the bar as the Tangerines led at halftime.
The hosts were even on 48 minutes as Ferguson beat rights back Dujon Sterling and shooting with his weaker right foot, the ball taking a deflection on its way in.
After Joshua Bowler fired wide, Grey gave Pools the lead at the other end as Blackpool couldn't get out of their own half, Crawford playing in the 19-year-old, who finished from 14 yards.
Christopher Hamilton spurned two glorious chances for the visitors, first going wide on the break and an even better chance also was wide seconds later.
Blackpool kept pressing for an equaliser, Slavery heading wide from a Hamilton cross two minutes from time. Three corners amounted to nothing as Hartlepool held on for a famous win.
Man of the match: Tom Crawford
He was one of the few bright spots in the first half and dominated in the second. He went on a great driving run and assisted Grey's winner. Overall, a fine performance.