The Minstermen had not won since New Year's Day and had embarked on a 16-game winless run which Worthington and his predecessor Gary Mills had preceded over.
However, against a Pilgrims side who themselves are battling to remain in the Football League, York struck twice in nine first-half minutes through Ashley Chambers and Richard Cresswell to record an overdue win.
When asked what the overriding feeling was among the York camp after the game, Worthington said: "It's one of delight because of the performance achieved to get the three points and it puts the marker down that what we're looking for, we can do."
Worthington thought his men built on their strong defensive performance in the 0-0 draw with Bristol Rovers on Saturday and backed his squad to go on an unbeaten run which would ensure their survival following last season's promotion.
"No doubt it was important to try and get the three points to continue that run - it makes an imprint in the players' mind," he added.
"To get that performance, and the result and control the game in the way we did was very, very reassuring and gives them a great platform."
The victory moves York just one point from safety as they looked to avoid an immediate return to non-league football, and Worthington concluded: "We've got a fighting chance and that's what it is. It was a fight from 10 games, there's now four left and every one will be important."