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Panthers, who also won the Challenge Cup this season, led at the end of the first period thanks to a fierce hit by Stephen Schultz from the blue line.
Blaze goaltender Brian Stewart made numerous saves to keep his side in the match going into the closing stages.
But Schultz teed up Kevin Quick to fire the second into the roof of the net.
Panthers keeper Miika Wiikman was then able to see out a 30-save shut-out, most notable for fine saves from Ashley Tait and Mike Quesnele.
However, Nottingham were good value for their victory and could easily have won by a greater margin had it not been for Stewart.
The Canadian also saved short-handed breakaways from Brad Moran and Evan Mosey and made an incredible stop to thwart Juraj Kolnik.
Earlier, Cardiff Devils thrashed Fife Flyers 6-0 in the third and fourth place play-off.
Nottingham Panthers secured their fifth play-off title of the Elite League era by beating Coventry Blaze in a nervy final at the National Ice Centre.