With a crash involving 2018 Tour champion Geraint Thomas causing mayhem 1.7km from the end of the 194km opening stage, Team Jumbo Visna rider Teunissen seized his chance for glory.
He also becomes the 267th ever yellow jersey wearer on the centenary of the introduction of the overall leader's jersey.
Lotto-Soudal's Caleb Ewan came home third with Team Dimension Data's Italian sprinter Giacomo Nizzolo - selected ahead of Mark Cavendish - finishing fourth.
Cavendish thought he was ready to build on his 30 Tour stage wins.
"After the sixth stage I will see how I feel", he said. "It's only because the riders were nervous that it was risky".
Nibali, the 34-yaer-old Bahrain-Merida rider, won the 2014 edition and with four-time champion Chris Froome absent after a horror smash he is one of the names expected to be in the mix for the yellow jersey. "If my condition is fine, I will fight for the General Classification".
"I gave myself enough space and avoided the actual crash but with the barriers there was nowhere to go".
"The main thing is that it didn't do any damage - the bike took the hit and I just toppled over".
Because the race was inside the last 3km, however, they lost no time and Thomas, whose preparations were hampered by a crash at the Tour de Suisse, was okay.
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"He's had three stitches to the eyebrow and he needs an x-ray to check out his knee", Astana's team director Alexandre Vinokourov revealed.
Stage two of the Tour de France is on Sunday July 7, 2019. As I have done for my entire career, I targeted a specific time to be at peak form. After a long, hard fightback from trying to compete for the whole of last season with Epstein-Barr Virus and after following a specific training program to peak in July, I feel I was in the ideal place.
"Now I have this lovely jersey and no-one can ever take it away from me", said the ecstatic victor.
Teunissen did not get carried away with his win, though, and promised to keep working for Groenewegen if he recovers well. "Hopefully when Dylan heard it was me who won he could still smile".
"It was a really odd day".
Michael Woods of Ottawa was 87th while Hugo Houle of Sainte-Perpetue, Que., was 91st.
This was just the second time that Le Tour has started in Brussels, which first staged the Grand Depart in 1958.
This year is the 50th anniversary of Brussels native Eddy Merckx's five Tour de France titles and the 74-year-old marked the occasion by sending the 176 riders on their way from the majestic Grand Place where fans chanted "Eddy Eddy".
The quartet reached the first difficulty of the day - the Muur van Geraardsbergen, a 1.2-kilometre cobbled climb - with a 3-minute lead. Belgian rider Xandro Meurisse, a member of the initial breakaway, was first at the Bosberg, another climb featuring at the Ronde van Vlaanderen classic race. But the Frenchman's efforts on open stretches of road exposed to wind were left unrewarded and he was ultimately swallowed up as the final sprint took shape.