The South Americans, playing bright and positive football, went close to an opener in the 24th minute when a thundering 35-metre free kick from Ronaldo Lucena crashed against the woodwork.
England, however, went in front after Calvert-Lewin won an aerial challenge on the edge of the box. His powerful first-time shot was parried out by keeper Wuilker Farinez but the Everton forward pounced to drive in the loose ball.
After the break, Woodman did well to come off his line and foil Sergio Cordova after a superb pass from substitute Yeferson Soteldo.
Tottenham Hotspur midfielder Josh Onomah, who was outstanding throughout, hit the bar with a powerful long-range effort after bursting through from midfield, but England then had a real scare at the other end.
England defender Jake Clarke-Salter was ruled to have brought down Penaranda inside the area, a decision confirmed by the video assistant referee, but Woodman produced a brilliant one-handed save to keep out Penaranda's spot-kick.
Venezuela pushed forward in the latter stages but Paul Simpson's side held firm to give England their first world title since their World Cup victory 51 years ago.
(Reporting by Simon Evans; Editing by Toby Davis)
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