Top scorer Michael Smith set up both goals as Wiles and Shane Ferguson did the damage at Portman Road.
And victory ensured Paul Warne’s side continued their remarkable recent run of form as they went an impressive 15th game without defeat in all competitions.
The visitors defended well as they limited the Tractor Boys to very little.
Striker Smith, who missed Saturday’s win through suspension, returned to the starting line-up as Warne made a four changes from the win against Cambridge United.
The Millers started brightly and Jack Walton had to be alert to tip Jamie Lindsay’s effort over the bar. But Wiles opened the scoring after 24 minutes with his seventh goal of the season. It was a wonderful 20-yard effort which deservedly handed them the lead.
It could have been two moments later when Smith had his effort blocked, before the hosts scrambled away the danger.
Freddie Ladapo squandered a chance as he fired wide after being slipped in by strike partner Smith. But Ferguson fired the visitors two goals to the good just before the hour from a tight angle.
Ipswich Town: Walton, Donacien, Nsiala, Edmundson, Clements (Penney, 63), Morsy, Evans (Edwards, 63), Chaplin (Pigott, 73), Celina, Fraser, Bonne. Unused substitutes: Hladky, Harper, Vincent-Young, Burgess.
Rotherham: Vickers, Edmonds-Green, Wood, Ihiekwe, Barlaser, Ogbene (Miller, 81), Lindsay, Wiles, Ferguson (Harding, 81), Ladapo (Sadlier, 86), Smith. Unused substitutes: Odoffin, Miller, Kayode, Grigg.
Referee: G Ward (Birmingham).