England needed a strong finish to see off the Argentinians, coming from 5-0 and 10-5 down.
Facundo Panceyra Garrido scored the opening try and, after Dan Norton had crossed for England, Diego Palma put the South Americans 10-5 in front early in the second period.
But Rob Vickerman and Mat Turner added further tries for England, both converted by Tom Mitchell, to see them home.
The result left them second in Pool A on points difference behind Samoa, who were 19-7 winners in their clash with Kenya.
England coach Ben Ryan was impressed with his side's display.
"I'm very happy with the result and the margin," he said on www.rfu.com.
"We always find it hard against Argentina, they worked very hard against us and a nine-point victory is rare against them - we normally scrape it by a score or less.
"They've been a bit of a nemesis for us and if you make a mistake you're going to pay."
Try-scorer Turner added: "We needed to find out that we have the ability to defend for long periods of time and then strike when we had to.
"All three teams we play are sides that are good at keeping the ball and you have to let them do what they do and then take that chance with both hands."
England face Kenya and Samoa on Saturday as they look to book their place in Sunday's quarter-finals.
Meanwhile, defending champions New Zealand, who beat England in the final last year, started with a 29-5 win over the United States in Pool B, while South Africa scored a brace of tries as they beat Wales 10-0.
In Pool C, Fiji beat Scotland 39-5. Fiji ran in seven tries, while Scotland's lone score came courtesy of Michael Fedo and briefly got them back to 7-5.
Australia defeated France 31-10.
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