Doets had won in the first round against compatriot Noa-Lynn van Leuven. The 28-year-old from Beverwijk was the first Dutch woman ever to appear in the title fight of the professional association PDC at London's Alexandra Palace.
Doets took the lead in the fifth set by winning the first leg. He threw 100 out. Then he also won the leg that he was allowed to start himself. At 2-1 in legs, he got the first match dart but missed.
Smith levelled the score and did so again, where in the fifth set he had to win by two legs. Doets then came back to 4-4. He extended his lead to 5-4 and got three darts on 40. He finished it off with the third dart.
Last year, Doets was stranded in the second round during his debut at the World Championship. At that time, defending champion Smith got the better of him.
"I had the feeling that he was really out of reach," Doets said at Viaplay.
"I never had the feeling that I was going to lose. I had that focus that I didn't have last time. I kept going."
Doets did admit that he panicked after his misses on double 20 and double 10.
"I let go of the arrow and thought, please. This was the best match of my life."
Earlier in the evening, Welshman Nick Kenny, Canadian Matt Campbell and Englishman Scott Williams reached the second round.
Kenny beat American Stowe Buntz 3-0, while Campbell defeated veteran Mensur Suljovic of Austria 3-2. Williams was too strong for German Niko Springer 3-1.
During the afternoon session, there was already a surprise with the victory of Robert Owen from Wales over Gabriel Clemens from Germany. Owen won 3-1.