Jonny May had already crossed for the first of England's six tries when Tomas Lavanini saw red for a high tackle on Owen Farrell in the 17th minute.
The second-row forward led with the shoulder and also caught the England captain around the neck, leaving referee Nigel Owens with little choice but to send him off.
The dismissal came with the score at 5-3 but effectively ended the clash of the top-tier nations as a contest, with Eddie Jones' side capitalising on the extra space to run out a comfortable winner.
Elliot Daly reached the line despite a juggling act with the ball, while Ben Youngs produced a burst from the base of a ruck before half-time, the scrum half having also crossed against the Pumas in the 2011 tournament.
Farrell struggled with his kicking, missing his first four attempts at the posts in the first half to leave the score at 15-3, yet his profligacy off the tee was never going to prove costly in the final reckoning.
The centre did land the extras after George Ford forced his way over from close range and a further penalty made it 25-3 after 53 minutes, raising the possibility of a second-half avalanche of points from England.
Instead it eased up, allowing Argentina to grab a consolation try through Matias Moroni after an excellent lineout move.
Conceding sparked England into life again, however, as substitute Jack Nowell marked his first appearance back from injury with a smart finish in the right corner before the pack carried Luke Cowan-Dickie over the line.
Top spot in Pool C will be up for grabs when England takes on France in Yokohama next weekend. Argentina, meanwhile, completes its round-robin fixtures by facing United States on Wednesday.