The Wolverhampton Wanderers loanee got forward from defence to rifle home a fine long-range effort, earning the Sulphurites a 1-0 success and their first victory of the summer.
Richards, 20, initially joined League Two Town in January this year, though his first loan spell at Wetherby Road was interrupted by and then eventually cut short due to injury.
But, having shown glimpses of his ability as a ball-playing defender during eight appearances last term, he says he is determined to contribute even more this time around.
"I've come back because I've got unfinished business," Richards told the Harrogate Advertiser.
"I feel like my time here was cut short and I just want to help the team out as much as possible. I was devastated to miss the end of last season, but hopefully I am back. I feel good.
"It's been a good start to pre-season for me. The position [on the left of a back-three] suits my game because it allows me to step in and play, but I also like defending one-versus-one and it allows me to do that as well.
"I don't mind playing at wing-back either, it doesn't bother we where I'm playing. I like both."
On his goal against the Terriers, which settled Saturday's contest, Richards added: "I've watched it back once or twice. I saw the opportunity to shoot and just thought 'why not? Let's have a crack'.
"I was looking and normally there's a guy in the way but there was a bit of a space. It was a good feeling when it hit the back of the net, I was happy.
"It's not the best goal that I've scored. Back in the day for Wolves I got a free-kick against Leicester, whipped it in the top bin."
Town's opening two pre-season friendlies saw them beaten 2-0 by League One Sheffield Wednesday, then 3-0 by Championship Rotherham United.
But, Richards says that beating a second-tier outfit featuring plenty of first-team players has immediately boosted confidence levels within the camp.
"I think it was important for confidence, even though it was a friendly, you still want to win," he continued.
"I thought we were really good. We stuck to the game-plan that the gaffer gave us. The clean-sheet is as good as a goal, to be fair, because as defenders, we love to defend.
"It's been a good start to pre-season and hopefully we can build momentum and just take it into the season."