Newcastle went into the match at St James' Park knowing they were already assured of going up after Nottingham Forest's failure to beat Cardiff City in a 0-0 draw earlier in the evening.
That result meant Newcastle were guaranteed to finish in one of the two automatic promotion places a year after their traumatic relegation from the top flight when local hero Alan Shearer, brought in for the last few desperate games of the season, failed to save them from the drop.
Chris Hughton, who replaced Shearer initially as interim manager before getting the job full time, told Sky Sports afterwards: "It's an incredible feeling, especially to do it here, in front of these supporters.
"We've still got the title to play for but its a real honour to be manager of this football club and bring Premier League football back to these supporters."
The "Toon Army" were already in high spirits before the kickoff, but were silenced when the visitors went ahead through Richard Cresswell after 22 minutes.
But they found their voices when Peter Lovekrands equalised with a 45th minute penalty and were ecstatic when Nolan scored the winner with a superb 73rd minute scissor-kick.
Newcastle have led the Championship for most of the season and moved to 89 points with five matches to play, six clear of West Bromwich Albion, who have four matches left and seem set to go up with them.
West Brom would have been promoted on Monday as well if they had won because of Forest's failure to win but the Baggies will have to wait after drawing 1-1 at Watford.
Forest stay third in the table with 72 points from 42 games, while Cardiff remain fourth on 69.
The draw at the City Ground ended Forest's club-record equalling sequence of 12 successive home league wins.
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