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Dagenham & Redbridge made the long trip back from the North East empty-handed after defeat at Victoria Park in their last match before Christmas.
Striker Ben House missed out with a sickness bug for Daggers, who were quickly on the attack but Alexander McQueen could not get his shot away in the box.
Kioso shot wide at the other end, as the home side began to enjoy more possession, but Chike Kandi then produced a run into the box, only to be denied by Raynes.
And Mitch Brundle brought the ball down well in the box from a Joan Luque corner, only to be crowded out by the home defence at the vital moment.
Shelton then fired over the bar from the edge of the box for Pools on 19 minutes, before McQueen tested Killip for the first time with a shot from range two minutes later.
An unmarked Donaldson was unable to direct a header at the far post back towards Toure on 26 minutes, while Elliot Justham tipped a long-range attempt by Josh Hawkes over his crossbar moments later.
And Toure fired well wide of the mark after working some space for himself in the box, before Justham pushed out another Hawkes effort.
Kandi forced a mistake from Liddle, but Killip raced out to clear the danger, before Brundle was caught by a flailing arm and a 2-on-1 chance for Luque and Kandi went begging.
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Kioso headed over from a Hartlepool corner four minutes before the break, then saw a dangerous cross Toure flash past him in stoppage time.
Good work by Joe Quigley set up a chance for Luque, who smashed wide five minutes into the second half, and Quigley was then denied himself by a good save from Killip.
But Justham had to produce a superb save to tip a Toure header around the post on 54 minutes to keep the scoreline blank, with Featherstone dragging a shot wide moments later.
Toure fired straight at Justham from range on 63 minutes, then had penalty claims waved away by the referee after a challenge from Kenny Clark.
But Pools broke the deadlock with 12 minutes remaining as Kitching's effort beat Justham.
And despite making three changes in the final quarter of an hour, Daggers could not get back on level terms.
Dagenham & Redbridge: Justham, Eleftheriou (Graham 75), Onariase, Clark, Stevenson, Brundle, Croll (D Wright 84), McQueen, Kandi, Luque (Grant 81), Quigley.
Unused subs: Seaden, W Wright.
Attendance: 3,259 (including 33 Daggers fans).