England's Nikita Parris had a first-half penalty saved by Vanina Correa, but Taylor got on the end of Beth Mead's cross in the 62nd minute to give her side their second straight win.
England coach Phil Neville had expected a tough game against an Argentina side who picked up their first World Cup point in a 0-0 draw against Japan in their opener and he was right.
England dominated possession as the Argentines soaked up the pressure early on and the Lionesses had a golden opportunity to go ahead in the 28th minute when Alex Greenwood was brought down in the area by Ruth Bravo but Parris's spot kick was saved.
Despite 11 attempts at goal, England were still looking for the breakthrough as they went in at halftime.
Correa again denied Parris early in the second half with a brilliant save from the forward's 20-metre strike, but there was nothing the 35-year-old could do when Taylor latched onto Mead's cross and tucked the ball away inside the box.
It was Taylor's first goal for England in 430 days, and it capped a relentless all-out attacking performance by a team who finished third in the previous World Cup.
Italy's Cristiana Girelli bagged a hat-trick and substitute Aurora Galli struck twice as they thrashed Jamaica 5-0 to qualify for the last 16 of the women’s World Cup on Friday.
Japan have four points after they beat Scotland 2-1 earlier on the same day, leaving the Scots without a point from two games.
