Leading 2-0 from Saturday's semi-final first leg, they did just enough to see off a spirited MK Dons side and despite losing 2-1 on the night, they will meet Sheffield United at Wembley on May 26 after a 3-2 aggregate success.
Jordan Rhodes' 40th goal of the season, a customary cool finish, after 18 minutes had sent Town 3-0 up on aggregate and put one foot in the final.
Daniel Powell levelled on the night for MK Dons when he curled in superbly six minutes before the break, setting them up for a second-half onslaught.
But it never materialised and by the time Alan Smith headed home at the back post late into added time to give them a 2-1 win it was too late, with Town holding on.
And Grayson wants Town to finish the job against Danny Wilson's Blades.
"We could have killed the game off with the chances we had," he said. "You could see extra time coming a mile off, Alan Smith coming on, getting booed all night and scoring the goal.
"Fortunately there was only one minute left and we saw it out comfortably enough.
"We are delighted with the end product. It has the ingredients of being a great game, obviously there is Yorkshire pride at stake but there is a bigger prize on offer of a ticket into the Championship.
"We will go there in good spirits and focused on what we need to do. There is no point going to Wembley if you're not going to win it and that is our ambition to do that. We are going there to win it.
"Hopefully I can keep up my 100% record in the play-offs.
"It is a great occasion but there is only one thing that matters when you get to Wembley and that is winning because you might as well finish 15th in the division and be on holiday two weeks ago.
"We know what we need to do."
The Dons fell at the semi-final stage for a second successive season and were left to rue two missed chances from Charlie MacDonald either side of the break.
But, in truth, they did not test Huddersfield's substitute goalkeeper Alex Smithies until late in the game and their boss Karl Robinson could not hide his disappointment at another failure.
"I thought we were the better team over the two legs to be honest and I am gutted we haven't gone through.
"Jordan Rhodes has been the difference. I thought we were magnificent, and we just didn't have that luck.
"I am disappointed because I wanted to go to Wembley and I am desperate to get this club in the Championship, I feel I have let people down and come up short.
"But we're not in the same hemisphere as a club like Huddersfield, we are punching well above our weight and the gulf didn't even show today.
"Good luck to Huddersfield. They were excellent and I am a little bit jealous, but I am sick because I wanted to be walking out at Wembley with my team, but it wasn't to be."