The south coast side controlled both halves and failed to make their superiority pay.
Pompey striker Izale McLeod earned his side a penalty after 13 minutes when he went down under pressure from Preston's Chris Robertson but stepped up to blaze a fierce effort against the crossbar.
Jake Jervis was a constant menace for the hosts and a poor Preston corner gave him the opportunity to explode forward on the counterattack after 27 minutes.
The on-loan Birmingham youngster rifled a shot goalwards which was beaten behind by North End keeper Thorsten Stuckmann.
Preston nearly snatched the lead in the final minute of the first half when Joel Byrom created space for a strike but his effort was well saved by Pompey stopper Simon Eastwood, who jumped up quickly to smother Chris Beardsley's follow-up.
Scott Allan had Pompey's best attempt of the second half, but his powerful left-footed effort was beautifully tipped over by Stuckmann after 85 minutes.