Andy Monkhouse's second-half header cancelled out Carl Baker's early opening goal for the League One side.
City took the lead in the 12th minute when Franck Moussa found space on the right and slipped a square pass inside to Baker, whose first-time shot was blocked. But Moussa reacted quickly to return the loose ball back into the danger area and Baker, who scored in Coventry's 3-1 first-round win at AFC Wimbledon, netted with a brilliantly-taken volley.
The home side came out positively after the break and started to dictate the pace of the game.
Matty Dolan forced a foul from Jordan Clarke just outside the area in the 53rd minute but Simon Walton's disappointing free-kick was straight at goalkeeper Joe Murphy.
Christian Burgess went close with a header in the 57th minute after Pools won a free-kick near the corner flag on the right-hand side. Dolan's cross looked good but the defender's header flashed wide.
Hartlepool's leveller came in the 78th minute when Walton found substitute Jonathan Franks down the right with a quality ball, and the midfielder chipped a pin-point ball inside for Monkhouse who powered a header past Murphy.