Pools went into the game with one defeat in six while the Daggers had suffered a single reverse in nine.
The home side went in front after 12 minutes when Luke James intercepted a shot from distance and his effort rolled across the face of goal for James Poole to prod home.
But the Daggers had their chances to level. Scott Flinders saved well from Medy Elito and Jack Baldwin knocked a Zavon Hines shot off the line.
They made it 1-1 after 55 minutes courtesy of a fine individual effort from Hines, who cut across the Pools defence on the corner of the penalty area and unleashed an angled shot home.
They should have gone ahead when Rhys Murphy opted to pass to Hines to tap in, only to be denied by an immaculate saving tackle from Neil Austin.
And the hosts' winner came after 79 minutes, Matty Dolan's deep corner headed in at the far post by Andy Monkhouse.