Preston took the lead on 38 minutes from a goal from Will Hayhurst. Aaron Williams equalised for Walsall on 60 minutes. PNE re-took the lead five minutes later from Matt Dudley. Dudley scored his second of the night as PNE made it 3-1 on 77 minutes.
PNE have one match to play at home to Wigan and now have 56 points from 23 matches.
Burnley are second with 52 points from 21 matches. The Clarets are at home to Carlisle on Wednesday before also playing Wigan at home and finishing the season at Stockport.
Walsall are looking as if they will finish third and now have 48 points from 22 matches.