The visitors led their opponents by just one point in the League Two table before kick-off and took the lead thanks to Michael Coulson's header after 41 minutes.
The Minstermen should have doubled their advantage after the break only for Ryan Bowman to miss an open goal, but AFC Wimbledon failed to take advantage of the mistake.
For York it is now three wins from their last four games and they are within four points of the play-off places.
Worthington said: "It was important we didn't come here and get caught up in the 'Wimbledon way' they're very much in your face and very committed but we played our own game.
"That's part and parcel of football (that Coulson's been frustrated). He's kept his head down and worked hard and he's got his opportunity up front and put a great shift in.
"It (Bowman's miss) is all about your concentration. If you blink and take your eye off that ball that's what happens. It becomes too easy in the mind. You must stay 100 per cent focused until you finish the job off
"It's very, very important to build on this result. To come to AFC Wimbledon and go away with three points is very pleasing.
"It's important we get other people scoring outside of our strikers. It's important everybody chips in and I mean everybody in the 10.
"It's vital that we keep the momentum going, keep the belief and keep working hard."