At 22, Wu becomes the second-youngest winner of the title after Stephen Hendry and only the second Chinese player to lift the trophy, following Zhao Xintong.
It was only the fourth World Championship final at the Crucible to go to a deciding frame, and it turned on composure under pressure as the players swapped momentum into the evening.
Momentum swings as frames are shared
Leading 13-12 overnight, Wu struck first, punishing a loose safety by Murphy with a break of 88 to move two clear. Murphy responded immediately with 82.
The match tightened further in the next frame. Wu, well-placed to restore his advantage, broke down on 26 after missing a presentable red. Murphy stepped in with 43 to close the gap.
Before the mid-session interval came the first turning point, as both players missed chances. Wu let a simple red slip and Murphy built a 56-19 lead but could not finish it off. After a safety exchange, Wu cleared 41 to the black to steal the frame.
Murphy again hit back straight away. After Wu made 70 in the following frame, Murphy produced a 73 break, including a 65 clearance, to take it on the final black.
The next two frames were shared more cleanly: Wu with a 56 clearance and Murphy with the highest break of the session, 131.
Wu holds nerve to take title in decider
The closing stages came down to errors in key moments. In the 33rd frame, Murphy made 45 but missed a routine red, then Wu capitalised with a 91 clearance to lead 17-16.
Wu then had a chance to finish the match, opening the next frame strongly before missing a straightforward black on 43. Murphy took full advantage, clearing 75 to force a decider.
Murphy had the first opportunity in the final frame but broke down on eight after missing the black.
A brief safety exchange followed, and when Murphy failed to turn in a difficult reach, Wu stepped up and made 85 to secure the title.