Cody McDonald ensured Coventry finished a dour first half in front when he scored after 33 minutes.
The striker got the wrong side of Peter Hartley to latch on to Carl Baker's through ball and steer a composed finish into the bottom corner from seven yards - his first City goal since September.
Coventry should have doubled their lead when Scott Flinders parried Carl Baker's 73rd minute shot into the path of Gary McSheffrey six yards from goal, but McSheffrey failed to control after turning refusing to strike first time.
Coventry never looked comfortable despite their advantage but in truth Hartlepool created precious little.
Baker could have put the result beyond doubt in the last minute of normal time but his shot was well saved by Flinders after he twisted and turned his way past two defenders.
Pools failed to register a shot on target and have now not scored in any of their past four league games.