Ipswich had looked to be heading for a deserved win when Jason Scotland netted in the 58th minute.
But Simpson, making his first appearance since January, nodded in a delightful header five minutes from the end to extent Hull's unbeaten run in the league to eight matches.
Ipswich were without the services of on-loan Jimmy Bullard who was ruled out due to the terms of his deal from his parent club.
Source: PA
Source: PA