Italian Valentino Rossi celebrated becoming the first rider to make 350 grand prix starts across all categories by finishing second behind his team mate, 2.915 seconds behind, at the Termas de Rio Hondo circuit.
Britain's Cal Crutchlow had to save fuel towards the end but was third on a non-works LCR Honda.
Vinales, who won in Qatar last month, started sixth on the grid but was third by the end of the first lap. He passed Crutchlow for second on lap three and took the lead a lap later when Marquez fell at turn two.
Vinales has 50 points with Rossi second on 36.
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"It was a difficult race because I started quite good but already Marc was pushing so hard," said Vinales.
"So I was trying from the first lap to make my own pace, then I saw that he crashed and I was just thinking to bring all the points I can home because it was very important to achieve the maximum points today."
Marquez, on pole in Argentina for the fourth year in a row, had a lead of more than two seconds over the opening laps before the bike went from under him and dumped him in the gravel.
The Spaniard is now eighth in the championship with 13 points.
"I was feeling amazing with the bike, I was riding really good and I don't know why... sure I did some mistake but this kind of mistakes make me quite disappointed," he said with some understatement.
His team mate Dani Pedrosa later crashed out at the same place while Ducati riders Jorge Lorenzo and Andrea Dovizioso fell after tangles with other riders.
Nine-times world champion Rossi made a strong start from seventh place and shadowed Crutchlow before passing the Briton six laps from the end and then pulling away.
"On the grid my mechanic said to me: 'This is the 350, make a good race," grinned the 38-year-old.
Argentina was the 888th grand prix since the championship started in 1949, and the Italian has ridden in 39.4 percent of them. Of Rossi's total, 289 starts have been in the top category.
(Writing by Alan Baldwin in London, editing by Clare Fallon)
