George Burley's first return to Portman Road as a manager ended pointless, with his side sunk by a bizarre own goal.
Ipswich were leading by Darren Bent's first-minute strike when Youl Mawene needlessly fired into his own net, and despite Marcus Tudgay's goal, Town held on for the win.
Ipswich had the perfect start with a goal on 26 seconds, Bent lobbing Lee Grant after racing onto Ian Westlake's throughball.
Although Bent deserves praise for the finish, Grant made life easy for him by coming halfway out and then changing his mind leaving himself stranded.
Grant saved low shots from Tommy Miller and Bent as Ipswich threatened to pummel a struggling Derby side.
However, the game then went through a quiet spell, during which both sides lost a centre half to injury - Richard Naylor for Town and Michael Johnson for Derby.
Home sub Alan Mahon almost set up Bent with a low cross, before Derby skipper Ian Tayler fired in two powerful drives that fizzed narrowly wide.
Candido Costa almost surprised Davis with a free-kick from way out on the left, his effort beating the keeper but ending up in the side netting.
Jim Magilton lobbed over for Town and Shefki Kuqi threading a teasing Mahon cross wide, while Taylor sent another fierce shot over.
Town went 2-0 up on 69 minutes when Grant could only parry Bent's shot and Mawene rammed a loose ball into his own net, when he seemed to have time to clear.
Derby were given a life line when Tudgay lobbed Davis after latching onto an Adam Bolder header through, despite looking yards off-side.
Despite that scare home keeper Davis was not troubled again and indeed it was Town who went closer to scoring in the games closing moments.