Elliot Benyon fired the Gulls ahead after just six minutes, spinning on Jordan Chapell's shot to beat City goalkeeper Michael Ingham from 10 yards. Ingham could do nothing about Ryan Jarvis' winner, a thumping 20-yard drive into the top corner after 23 minutes.
York striker Richard Cresswell reduced the arrears with a 73rd-minute penalty after Torquay left-back, and last man, Thomas Cruise was sent-off for denying Josh Carson a goalscoring opportunity, but it was too little, too late for the Minstermen.
It was 19th-placed Torquay's second 2-1 home win in five days and moved them five points clear of second-bottom York with six games remaining.
"The game is 90 minutes long not 20 and you cannot afford to give the opposition a two-goal start because it's tough going getting back into it," Worthington said. "We gave away two very soft goals.
"But I thought they showed a lot of spirit and they passed the ball a lot better than we have been, which I was very pleased with.
"But we need a ruthless streak and more conviction around the opposition goal and I think that is down to self-belief, and when you have gone 15 matches without a win it's bound to have an effect on confidence.
"It's about being brave and taking the responsibility on and making it happen. There were a few situations where we could have made things happen and we didn't. You really have to make things happen in this game and if you wait for them to happen, they don't happen.
"Games are running down, time is running down so we need to do it sooner rather than later.
"There's six games left for us now. We need the points on the board and we have another long trip away to Bristol Rovers next weekend."