The Reign striker had come into the side in place of Manchester Citys Ellen White despite the latter scoring against Scotland in the opener. The decision to switch No9 however was repaid as Taylor struck the winner moments after the hour.
Departing City winger Nikita Parris had the opportunity to give England the lead in the first period but saw her penalty saved by Vanina Correa in a difficult opening 45 minutes for the Lionesses.
The Argentina stopper continued to spoil Englands night with a multitude of brilliant stops in a 30-minute spell following Parris penalty.
Taylor however ensured the Lionesses progression to the last 16 as she guided home a low cross to end her lengthy international drought.
England now battle Japan for top spot on Wednesday June 19 when they will seek a possibly easier tie in the last 16.
Taylor was one of a quartet of changes made by Phil Neville with Citys Karen Bardsley, Keira Walsh and White making way alongside Millie Bright. Uniteds Abbie McManus, who made her first start of the tournament, was joined in the 11 by goalkeeper Carly Telford, Jade Moore and the eventual match-winner Taylor.
Despite the 34 places between the two nations in the FIFA world rankings, the Lionesses struggled to break down the feisty Argentineans for much of a first half in which open space in the final third difficult to come by.
Argentina set up in compact fashion to frustrate England with a highly-regimented 4-5-1 in operation, ensuring the Lionesses would dominate possession but have to be patient when searching for chances.
They eventually found an opportunity to take the lead 27 minutes in from the spot when Uniteds Alex Greenwood was brought down in the area by Ruth Bravo as she raced towards the byline.
Lyon-bound winger Parris stepped up in search of her second-ever World Cup goal but failed to replicate the composure of her spot-kick against Scotland, with her weak side-footed effort palmed against the woodwork by Correa.
The Argentina keeper was again on hand to prevent England finding a breakthrough moments before the break as she saved well from Mead. The winger latched onto a Fran Kirby through ball but could only direct her shot straight at Correa as Nevilles side went into the break frustrated.
As Correas teammates began to tire, the chances continued to come for England following the interval with the brilliant Argentinean stopper continuing to thwart the Lionesses advances.
However, she could do little to stop Engand taking the lead on the hour mark as Taylor, Golden Boot winner at Euro 2017, struck her first of the tournament.