They felt New Zealand Residentials champion Simon Rea should have joined New Zealand No 1 Dan Willman in the main draw of the singles.
Nielsen's reply surely justified tournament director Graham Pearce's decision to go with the rankings in giving him another chance.
In a similar first-round upset in 1998, Nielsen beat Brazilian Fernando Meligeni before losing in the second to Marcelo Rios.
The last New Zealander to progress beyond the opening round was Brett Steven, who in 1999 was knocked out in the semifinals by eventual winner Sjeng Schalken, of the Netherlands, after Steven had knocked out Marat Safin a round earlier.
Russian Safin is top seed for this year's tournament.
Nielsen began tentatively. After racing to 40-0 he needed another nine points to serve it out.
Games then went with serve to 6-6, as Nielsen aces won a couple of key points.
Nielsen took the tiebreak 7-5 after the Swede had kept it alive with an ace at 3-6.
The only break of the match came in the fifth game of the second set. Nielsen hammered that advantage home taking the next game to love, again helped by an ace.
Despite a double fault - a point after serving his fourth ace - Nielsen wrapped up the 1h 28min tournament opener in the 10th game after failing to take any of five match-point opportunities in the previous game.
Vinciguerra left the court and, one suspects, the city, in a hurry, but Nielsen was understandably happy to talk about his unexpected triumph.
"He was not the biggest player but it was my biggest win," said Nielsen. "I played some shots at the right time.
"Sure, there was some pressure after getting the wildcard but I felt Auckland Tennis made the right decision. I was unhappy at failing to take those match-point chances but I sat down, thought about it and worked my way through the last game."
Asked when he thought he could win, Nielsen said: "Two days ago."
Nielsen's effort sparked Rea and Jacob Olsen, wildcards into the doubles, to try to match his effort.
Against Russian Andrei Olhovskiy and his Japanese partner, Thomas Shimada, the New Zealanders took the first set to a tiebreak and won the second 6-4 before losing in three.
It was a sterling effort by the youngsters, who had not played doubles together since their Auckland Grammar School days.
The 6-7 (4-7), 6-3, 3-6 loss ended their tournament and allows them to fly out today to continue their tennis careers at the University of Tennessee.
"We haven't been playing a heap together," said Rea. "But we enjoyed it out there. We were on a roll after the second set."
In the end, the greater experience of their opponents told.
Olhovskiy, once ranked the sixth-best doubles player in the world and the winner of 18 ATP doubles titles, and Shimada, who was ranked 40th in September last year, were too strong in the third set, winning the match in just inside two hours.
Hopes of a second New Zealander joining Nielsen in tomorrow's draw were dashed last night when United States-based Willman went down in straight sets to world No 50, Frenchman Jerome Golmard, 4-6, 1-6.
Willman, in his first Heineken Open, appeared nervous.
"It took me a long time to relax. I missed a lot of easy shots. But I enjoyed it out there. I would love to come back."
But the stats, in the end, told the story.
Golmard won 86 per cent of his points on his first serve, Willman only 51.
Golmard served six aces, Willman only two.
Today's schedule.-
Centre-court (from 11 am): Gilles Elseneer v Dominik Hrbarty, followed by - not before 12.30 pm - Marat Safin v Michael Chang, Jarkko Nieminen v Goran Ivanisevic, Jan-Michael Gambill v Francisco Clavet, followed by - not before 7 pm - Greg Rusedski v Mariano Zabaleta, Simon Aspelin/Andrew Kratzmann v Mark Nielsen/James Shortall.
Court four (from 11 am): Jiri Novak v Andrea Gaudenzi, Galo Blanco v Sjeng Schalken, Gaston Gaudio v Jonas Bjorkman, Stefan Koubek v Felix Mantilla.
Court six (from 11 am): Michel Kratochvil v Robby Ginepri, Albert Montanes v Mikhail Youzhny, Andre Sa v Michal Tabara, Bjorn Phau v David Nalbandian.
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