Blair raced onto an excellent Ashley Chambers pass midway through the second-half and chipped the ball over advancing goalkeeper Glyn Thompson for his nineteenth goal of the campaign.
Seven minutes later York wrapped it up when Chambers was again the provider following a fine Patrick McLaughlin through ball and Lanre Oyebanjo helped himself to any easy conversion at the far post.
Newport had earlier made the better start and Romone Rose should have put them ahead on nine minutes but shot too close to Michael Ingham after a quick break forward from a corner at the opposite end. Rose also drove over the target from around 30-yards.
Northern Ireland Under-21 international McLaughlin had an effort deflected narrowly wide in reply and Jon Challinor forced a low save from Thompson just before the break.
The Minstermen continued that improvement as they attacked towards their own supporters in the second-half and took the lead when Blair - who netted a last-minute winner at Luton Town in the semi-final - tucked home Chambers' 65th minute through ball.
And once Oyebanjo had added his third goal of the campaign with a simple tap in following more excellent work from Chambers the game appeared over for Newport despite Ismail Yakubu heading against an upright late on.
York must now repeat the outcome in their play-off final against Luton next week to mark a truly wonderful season.
"I hope it's the start of new things to come. It's a fantastic club and a fantastic city, with lovely, lovely people," delighted manager Gary Mills told The Press.
"We've worked hard to achieve what we want to achieve. The ultimate aim is to get out of this league, but we will talk about the trophy today.
"It feels great, it's wonderful, and I'm pleased for everybody."
York City: Ingham. Challinor, Smith, Gibson, Meredith, Parslow, Oyebanjo, McLaughlin (Fyfield 83), Blair, Walker (Reed 90), Chambers (Moké 90)
subs (unused): Musselwhite, Potts
Goals: Blair (65), Oyebanjo (72)
Newport County: Thompson, Pipe, Warren, Yakubu, Hughes, Foley, Porter (Knights 80), Rose (Harris 69), Evans, Jarvis (Buchanan 69), Minshull
subs (unused): Swan, Rodgers
Ref: A. Taylor