The Tigers started well and good play gave Jason Price a chance to run in on goal but Ipswich keeper Shane Supple did well as he rushed out to snatch the ball off Price's toe.
Chances continued to arrive for Hull as the Ipswich defence stood off the City front men and Billy Paynter tried to take advantage but he fired a 25-yard shot over the crossbar.
Ipswich substitute Danny Haynes had a chance to put his side ahead before the break but he couldn't convert a low cross from Ian Westlake inside the area.
Hull finished the first half the stronger team as Fagan had a free header inside the box but he couldn't get enough power on the ball as it was easily saved by Supple.
Leon Cort also had a chance inside the box minutes later but he could only poke the ball into Supple's hands.
Ipswich started brightly in the second half and could have been 1-0 up early on as Westlake flashed a shot just wide off Boaz Myhill's left-hand post.
A minute later Hull nearly went further ahead as a pin-point cross from Price gave Paynter a great chance but his header was matched by a good save.
The hosts did extend their lead on 70 minutes as a through ball from Damien Delaney sent Price through and his low ball across the six-yard box was tapped home by Fagan.
Darren Currie nearly reduced the deficit close to full-time but his strike from the edge of the area went inches wide of Myhill's right-hand post.