Paul Heckingbottom's side had the better of the action in the first half, with Daniel Jebbison twice going close, first when his shot was well blocked by the Ipswich defence, and again when he struck wide of the mark.
Ipswich came into the match off the back of four wins from their past five, however they were defeated by Sheffield United last time out, and they struggled to gain traction against the Lilywhites.
They fought back, however, when Wes Burns teed up Darnell Furlong, but his right-footed effort was nudged away by the Preston back line.
The visitors continued to threaten, with Ipswich keeper Christian Walton having to stay alert to deny Gibson's volley before the break.
In the second half, Preston maintained their momentum, with Alfie Devine's lofted effort going over the crossbar, while Jordan Thompson also went close with a long-range drive.
The breakthrough came with less than 20 minutes remaining as Gibson prospered from a corner and coolly tapped in from three yards out - but there was more drama to come.
Clarke was brought down in the box and duly dispatched his spot kick, awarded despite Preston's protests, as the hosts avoided a second consecutive defeat and kept in the fight for an immediate return to the Premier League.