Yorkshire all-rounder Pidcock, who rides on the road with Ineos Grenadiers, went past Swiss mountain bike great Nino Schurter near the end of the fifth lap in Glentress Forest.
The Olympic champion began to put the hammer down to distance Schurter on a climb on lap six.
Schurter was eventually overtaken by the strong-finishing Samuel Gaze of New Zealand who took silver, 19 seconds behind Pidcock. Schurter, bidding for an 11th world gold in the cross-country event, in the end hung on for the bronze.
Pidcock said a mechanical issue had made the last couple of laps stressful.
"It was a massive relief because as soon as I attacked my gears were jumping all over the place, I thought my race could be over at any moment," Pidcock said.
Fans had expected a duel between Schurter, Pidcock and road world champion Mathieu van der Poel, but the young Dutchman crashed out on the short opening lap.
Ferrand-Prevot completed a golden double when she outclassed the field to win the women's title for a fifth time.
The French rider attacked her compatriot Loana Lecomte on the second lap on a wet course and never looked back as she won by more than a minute.
Ferrand-Prevot also won the short track title this week.
"I'm feeling very happy. It was a super hard race, I didn't have a good start but I wanted to keep my own pace during all the race," she told reporters.
"It's what I did - full gas on the uphill and then I tried to recover on the downhill and it worked out perfectly. I'm proud of myself because I kept my plan even though I didn't have a good start. I just said: 'I have one mission today and I have to reach it'."
The all-rounder now has five world titles in the cross-country discipline which is the Olympic Games event.
Lecomte was second with Dutchwoman Puck Pieterse winning the scrap for the bronze medal.