Goddard finished fifth in the 200m individual medley – the event in which he is Commonwealth champion – in a time of 2:0.66 seconds to secure his place in the next round.
He has decided to compete only in the medley rather than double up with the 200m backstroke at the Olympics this summer, with his focus entirely on the event.
Laszlo Cseh heads the field into Wednesday's final, 1.64 seconds ahead of second-fastest qualifier Simon Sjoedin.
World record holder Paul Biedermann is looking to complete a double following Monday's victory in the 400m.
In another event,
Scozzoli took silver behind Dale Oen when the Norwegian won this event at last year's world championships in Shanghai -- his country's first such title in swimming.
Scozzoli touched in 1:0.55 seconds. Valeriy Dymo of Ukraine took silver in 1:00.68 and another Italian, Mattia Pesce, took bronze in 1:00.93.
"He accompanied all of my achievements and he accompanied me today, too, and I really wanted to win this to remember him," Scozzoli said.