The home side had the better of the first half but found themselves a goal behind when Kuqi struck with a left-foot volley from 25 yards.
He scored again from close range just after the break when Darren Bent threaded through a neat pass.
Ipswich manager Joe Royle:
"It's nice to win and nice to keep a clean sheet, especially when we haven't
been at our best.
"It was 60 minutes before we really got going. But we are averaging two goals
per game and that is not a bad habit to have. And Kuqi missed an easier chance
before he opened the scoring.
"I was delighted with the back four who just get better and better. Rotherham
never got behind us and Kelvin Davis only had one half save to make all
afternoon."
Rotherham: Pollitt, Stockdale, Swailes, Gilchrist,
Minto (Scott 57), Sedgwick (Warne 81), Mullin,
Garner (Vernazza 67), Shaw, Proctor, Richard Barker.
Subs Not Used: Montgomery, McLaren.
Booked: Swailes, Mullin.
Ipswich: Davis, Wilnis, De Vos, Diallo, Naylor,
Magilton (Dinning 76), Miller, Horlock, Westlake, Kuqi,
Bent (Bowditch 70).
Subs Not Used: Counago, Barron, Price.
Booked: Naylor, De Vos
Goals: Kuqi 43, 47.
Att: 5,504.
Ref: G Laws (Tyne & Wear).