During an exciting last fifth set Heydon hit a stunning 132 checkout to level the match at 3-3, while Veenstra was waiting on a double to throw for the match.
'The Undertaker' took a 5-4 lead, but the Dutchman forced a legdecider as he hit a 13-dart leg against the throw. Veenstra took the advance to start the last leg and claimed victory with a 35 finish.
Veenstra, a former Lakeside semi-finalist, takes on Scott Waites in the second round. The number eight seed defeated Jeffrey van Egdom with 3-1 in sets. Krzysztof Kciuk beat Brian Lokken from Denmark in the Preliminary Round.
There was another shock in the ladies event as Maria O'Brien overcame Deta Hedman with 2-0 in sets. Four-time ladies World Champion Lisa Ashton was beaten by Mikuru Suzuki on Saturday, as the number two and third seed are out of the tournament.
Click here for more information about the 2019 BDO Lakeside World Championship.
Scott Waites (86.55) 3-1 (82.08) Jeffrey Van Egdom
Brian Lokken (77.16) 1-3 (79.38) Krzysztof Kciuk
Deta Hedman (67.53) 0-2 (70.80) Maria O'Brien
Richard Veenstra (89.67) 3-2 (93.09) Nigel Heydon
19:00 Roger Janssen Vs Wouter Vaes
20:15 – Fallon Sherrock Vs Corrine Hammond
20:45 – Mark McGrath Vs Adam Smith-Neale
22:00 - Wayne Warren Vs Mark Layton
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