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Coventry City 2-1 Hartlepool United
Coventry striker Leon Clarke hit a stoppage-time winner just minutes after Hartlepool defender Jack Baldwin looked like he had forced extra time.
The Sky Blues led at the break, Clarke latching on to a John Fleck through ball before calmly slotting home.
They continued to have the better of the play, but Pools goalkeeper Scott Flinders was in top form.
Baldwin rose highest from Matty Dolan's corner to equalise, but Clarke struck from inside the box in the 93rd minute.
Coventry now face an FA Cup third-round trip to Barnsley.