Everton striker Calvert-Lewin became the third England player to score in a World Cup final after Geoff Hurst and Martin Peters in 1966 -- the last time England won any world title.
The Young Lions had to withstand a ferocious second-half onslaught with goalkeeper Woodman saving a penalty from Venezuela's Adalberto Penaranda 16 minutes from the end.
England had the better of the early exchanges with Liverpool-bound Dominic Solanke forcing a save from Wuilker Farinez and seeing a long-range effort go wide in the opening quarter of an hour.
There seemed no danger as he prepared to take a free-kick from the edge of the centre circle but his fierce swerving drive took Woodman by surprise as it smashed into the post from fully 40 metres out.
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Calvert-Lewin had already come close with a header when he scored what proved to be the winner in the 35th minute.
The striker rose to beat Nahuel Ferraresi to high ball on the edge of the box and saw his right-foot shot parried by Farinez.
Venezuela took control after half-time as England defended deep and tried to hit on the counter.
The tiny but lively substitute Yeferson Soteldo, who stands just 5ft 3in (160cm) tall, energised his side and immediately sent in Sergio Cordova to force a fine save from Woodman one-on-one.
England still had an attacking threat and Josh Onomah almost gave them a two-goal cushion when he ran unopposed to shoot from distance, only to see his shot cannon back off the crossbar.
Venezuela's increasing pressure finally paid off when Penaranda was brought down by Jake Clarke-Salter and the referee Bjorn Kuipers pointed to the spot, with his decision confirmed by video review.