Rhodes, 22, English football's 40-goal top scorer last season while in League One, finished superbly for Huddersfield's second-half clincher.
The Scotland international has been tracked by clubs in the Premier League and the Championship for months, and Huddersfield's determination to hold onto their prized asset is likely to be tested in the last week of the transfer window.
Town have put a reported ?8million price on his head, with chairman Dean Hoyle insisting he will not sell to a Championship rival.
Rhodes, who scored a stoppage-time penalty equaliser against Nottingham Forest on Tuesday, smashed a 58th-minute shot into the top corner after James Vaughan had caused problems in the box.
"Jordan's price has just gone up with that goal," beamed Grayson.
"We have no intention of selling him until someone meets our valuation.
"Like any other player in the world, Jordan Rhodes has his valuation but we don't want to sell him.
"The chairman has turned down a lot of money already and all Jordan has to do is keep working hard in training every day and hopefully score goals.
"If he does, then it may be that a top Premier League club comes in for him in January."
Town, winning for the first time at Championship level in 11 years, made the perfect start when centre-back Joel Lynch headed his first goal for the club in the seventh minute.
Vaughan, who joined on a season-long loan from Norwich on Friday, won the corner and boyhood Burnley fan Oliver Norwood launched the set-piece for Lynch to head home despite an attempt to clear it off the line.
Joseph Mills thought he had kept the ball out but the assistant referee gave the goal.
Rhodes struck the bar with a header and forced Lee Grant into a point-blank save.
Burnley lacked punch up front but thought they had equalised when David Edgar's shot was touched in by Charlie Austin, but referee David Webb ruled it out for off-side.
Rhodes sealed it after the break and though the Clarets pressed, they failed to make a serious attempt on the Huddersfield goal.
Grayson insisted his side were far from a one-man team and added: "It was a real good team performance with some good individual performances.
"We closed down well, passed the ball well and were resolute and we have a threat going forward.
"I didn't see whether the ball went in for the first goal but the linesman has made a decision.
"It's important to get your first win for the confidence it gives you going forward. We have set our standards and we must keep them up. We are the underdogs in this league and must be on our guard."
Burnley boss Eddie Howe said: "I need to see the first goal again and also our disallowed goal.
"Joe Mills thought he had kept the first one out and for our effort the ball nicked Charlie but it didn't look like he was beyond the defender."
Howe was concerned that his side conceded from set-pieces and said: "That is not like us. It was a bad day from that point of view.
"In the final third we lacked a bit of spark and invention and did not have an end product.
"I thought we dominated possession and we hoped to create chances and score goals but it didn't happen."
Burnley lost back-to-back games for the first time since March and Howe said: "In this league you have to bounce back.
"This league is very difficult and we have to make sure we are tougher to beat."
