Lock Joe Launchbury, centre Billy Twelvetrees and winger Chris Ashton crossed the line to put the hosts, bristling with attacking intent, 24-6 ahead at halftime.
England, who fought back to beat Australia 20-13 last Saturday, struggled to maintain their momentum and Nicolas Sanchez kicked two penalties to reduce the deficit for the Pumas.
But England replacement number eight Ben Morgan stormed over with a barrelling 20-metre run late on and the hosts completed a comfortable win to put themselves in good heart for next week's game against world champions New Zealand.
"Overall there were plenty of positives," England coach Stuart Lancaster told a news conference.
"We started the game very brightly, our intent was good and our accuracy was good but we fell away in the second half.
"The players are pleased overall with the performance but we are not jumping up and down because we know we have a tough game next week."
After flyhalfs Owen Farrell and Sanchez had exchanged early penalties, the England forwards started to dominate.
They twice went close to crossing the line and a third driving maul enabled Launchbury to touch down for the game's first try.
England tried to run the ball at every opportunity and following another spell of pressure centre Twelvetrees carved his way over, Farrell's conversion stretching the hosts' lead to 17-6.
England won another lineout five metres from the Argentina line, Farrell's slick pass released winger Ashton to touch down in the right corner and the flyhalf kicked a difficult conversion from the touchline to extend the advantage to 24-6.
Alex Corbisiero replaced Joe Marler at prop after the interval and England started the second half by conceding two sloppy penalties which Sanchez kicked to reduce Argentina's deficit.
Both teams made a raft or substitutions and Argentina coped better as England failed to retain the possession they had enjoyed in the early part of the game and made a string of basic errors.
Argentina centre Marcelo Bosch missed a penalty that would have cut the lead to nine points but England rallied in the closing stages, Morgan bursting through a tired defence and surging over the line to send the crowd home happy.
"The first half was bad for us, we couldn't handle the ball and couldn't put on the pitch what we'd done in the week and that happens," Argentina captain Juan Manuel Leguizamon said.
"We talked at halftime and said we should go out and show some character and personality and we did it. We still have a lot of work to do. We thought in the second half we could win it. We put pressure on England."
