After the Lilywhites had fallen 2-0 behind at Deepdale, Barkhuizen started the fightback with a close-range header from Sean Maguire's knockdown.
Daniel Johnson equalised from the penalty spot before Barkhuizen hit a superb winner eight minutes from time, running on to a pass from Alan Browne and curling a first-time shot into the top corner from the left-hand side of the box.
Barkhuizen has now scored seven goals this season, five of them in the Championship.
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It was a good week for him, with the 26-year-old also finding the net in the 1-1 draw with Leeds United last week.
Former North End striker Eoin Doyle was also included in the team of the weekend.
Doyle netted a hat-trick for Swindon Town in their 4-0 win at Crawley Town on Saturday and has scored 13 goals in 13 League Two starts since joining the Wiltshire club on loan in August.
