The summer signing from Scunthorpe struck in the 18th minute with a clinical right-footed finish after a fine cross from Billy Jones.
It was his third goal of the season and proved enough to secure the points for Darren Ferguson's men, who had lost their opening two matches of the season without finding the net.
Progress has been slow at Deepdale since Ferguson replaced Alan Irvine at the turn of the year but their campaign is at least up and running.
The result lifted Preston above Portsmouth, who look destined for a long season after collecting one point from their opening three matches.
North End could have led in the seventh minute when Paul Coutts was afforded the time and space to blaze wildly over the crossbar from close range.
Pompey threatened in the 11th minute when Marc Wilson hit a 30-yard shot which drew a fine block from Coutts.
Wilson tried his luck from distance again moments later but Hayes' opener from Jones' delivery put Preston in control.
Former Deepdale favourite David Nugent fired over the crossbar from the edge of the penalty area in the 18th minute and Portsmouth midfielder Michael Brown missed the target from 25 yards.
Hayes and on-loan Manchester United midfielder Matty James also went close for the hosts before the break as Preston struggled to translate their dominance into goals.
Pompey striker Tommy Smith went close for the visitors shortly after the break but Hayes should have added a second for Preston in the 58th minute only to volley wide when well placed.
The hosts went even closer shortly before the hour mark when 18-year-old striker Josh King - also on loan from Old Trafford - fired goalwards from inside the penalty box, forcing visiting goalkeeper Jamie Ashdown into a smart stop.
In the 69th minute, James brought another impressive save from Ashdown with a fierce close-range shot.
Portsmouth sought to find a response as Carl Dickinson rifled in a shot from distance which Danny Mayor did well to clear.
The visitors threatened again in the 75th minute when Ibrahima Sonko headed wide from six yards out.
King then forced Ashdown into another superb save and Keith Treacy also went close as the hosts finished the stronger.