Steph Houghton and Jill Scott were in from the start as the Lionesses overcame stubborn opposition, with former Melbourne City striker Jodie Taylor netting the match-winner after Nikita Parris had a penalty saved.
City and England’s skipper was rarely tested, but Scott was typically tireless and it was her surging run which allowed Alex Greenwood to deliver an inviting cross for Taylor to tap home after 61 minutes.
The goal sent the Lionesses top of Group D, with six points from a possible six, two ahead of second-placed Japan.
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Facing an Argentina whose aim was to contain, England dominated possession and Houghton had little to do defensively.
Scott, by contrast, got through a mountain of midfield work.
The 32-year-old sent an early effort into Vanina Correa’s hands before La Albiceleste’s keeper palmed Parris’ penalty onto the post, after Ruth Bravo upended Greenwood.
Correa was in inspired form, her outstretched leg kept out Beth Mead’s low drive, before she got a strong hand to Parris' fierce effort as England’s frustrations grew.
But that was eased on the hour mark.
Scott powered through midfield and offloaded to Fran Kirby to start the move which led to Taylor’s goal and the City stalwart may have doubled the lead if not for sending two headers over the bar.
One goal proved enough, however for England to secure a place in the knockout stage with one game to spare in Group D.
They face Japan at 8pm (BST) on Wednesday 19 June, knowing a draw would send them through to the last 16 as group winners.
Fans in the UK will be able to watch that game live on BBC One, with coverage starting at 7.30pm (BST).