Keane's men began to build up a head of steam and in the 20th minute Rory Fallon collected possession 20 yards from goal and drilled in a fierce shot which Andy Lonergan did well to tip round a post.
In the 28th minute an inswinging corner from Danny Pugh was greeted by Billy Jones and his firm header from six yards out struck a post.
Tommy Smith headed wide for Ipswich and Hume then blazed over the crossbar from 12 yards but he was not so wasteful five minutes after the restart.
Jon Parkin showed delightful footwork to cut the ball back for Hume to fire home a low right-foot finish from 12 yards.
Parkin then hit an 18-yard shot which Brian Murphy did well to save before Michael Tonge had a shot blocked by Mark Kennedy as Preston went in search of a killer second goal.
In the 68th minute, Ipswich's Troy Brown headed goalwards from 12 yards but Lonergan was again equal to the effort and saved comfortably.
Keane brought on Jaime Peters and he met a cross from Jack Colback with a firm header that Lonergan superbly tipped around a post as Preston held on.