Town keeper Marton Fulop kept the visitors in it at the break with a series of fine saves to single-handedly deny the hosts.
The Hungarian continued to work his magic after the break but Ipswich were a much livelier attacking threat and his saves proved crucial as Jimmy Bullard struck a well-taken brace to clinch three impressive points.
Jewell said: "I am delighted with the result and our second-half performance, but disappointed with the first half when we were very poor.
"I lost my temper with my players at half-time but it seemed to work as we were much stronger than Cardiff in the second half.
"We have overcome a poor start to the game to win but we have to believe we can compete at this level. We sat off Cardiff in the first half and it looked as though we were expecting to lose so half-time came at the right moment."
Source: PA
Source: PA